Search

The notion of stationary equilibrium is one of the most crucial solution concepts in stochastic games. However, a stochastic game can have multiple stationary equilibria, some of which may be unstable or counterintuitive. As a refinement of stationary equilibrium, we extend the concept of perfect equilibrium in strategic games to stochastic games and formulate the notion of perfect stationary equilibrium (PeSE). To further promote its applications, we develop a differentiable homotopy method to compute such an equilibrium. We incorporate vanishing logarithmic barrier terms into the payoff functions, thereby constituting a logarithmic-barrier stochastic game. As a result of this barrier game, we attain a continuously differentiable homotopy system. To reduce the number of variables in the homotopy system, we eliminate the Bellman equations through a replacement of variables and derive an equivalent system. We use the equivalent system to establish the existence of a smooth path, which starts from an arbitrary total mixed strategy profile and ends at a PeSE. Extensive numerical experiments, including relevant applications like dynamic oligopoly models and dynamic legislative voting, further affirm the effectiveness and efficiency of the method. [ABSTRACT FROM AUTHOR]

The concept of perfect equilibrium, formulated by Selten (Int J Game Theory 4:25–55, 1975), serves as an effective characterization of rationality in strategy perturbation. In our study, we propose a modified version of perfect equilibrium that incorporates perturbation control parameters. To match the beliefs with the equilibrium choice probabilities, the logistic quantal response equilibrium (logistic QRE) was established by McKelvey and Palfrey (Games Econ Behav 10:6–38, 1995), which is only able to select a Nash equilibrium. By introducing a linear combination between a mixed strategy profile and a given vector with positive elements, this paper develops a variant of the logistic QRE for the selection of the special version of perfect equilibrium. Expanding upon this variant, we construct an equilibrium system that incorporates an exponential function of an extra variable. Through rigorous error-bound analysis, we demonstrate that the solution set of this equilibrium system leads to a perfect equilibrium as the extra variable approaches zero. Consequently, we establish the existence of a smooth path to a perfect equilibrium and employ an exponential transformation of variables to ensure numerical stability. To make a numerical comparison, we capitalize on a variant of the square-root QRE, which yields another smooth path to a perfect equilibrium. Numerical results further verify the effectiveness and efficiency of the proposed differentiable path-following methods. [ABSTRACT FROM AUTHOR]

Although many product providers deem user contributions (e.g. online reviews) important, providers often struggle to obtain them, i.e. most users are lurkers who are reluctant to post reviews. This study is conducted to understand better how to delurk users by investigating the role of user stickiness in review posting behaviour. By employing a large-scale dataset from TapTap, a Chinese mobile game community, and conducting a multimethod investigation, this study found that sticky users with a product are more likely to engage in review posting behaviour related to the product. Also, this positive stickiness-post effect varies for some user and product features: (a) the positive relationship between user stickiness and posting behaviour will be strengthened as user expertise rises, (b) the positive stickiness-post relationship will be alleviated when products are collaborative-consuming products (vs. private-consuming products), (c) and the positive stickiness effect on review posting behaviour will be stronger when product providers are small-scale (vs. large-scale). These findings provide a comprehensive understanding of biases in lurking/posting behaviour related to user stickiness and help product providers gain insights into delurking users and gathering user intelligence. [ABSTRACT FROM AUTHOR]

The concept of proper equilibrium was established as a strict refinement of perfect equilibrium. This establishment has significantly advanced the development of game theory and its applications. Nonetheless, it remains a challenging problem to compute such an equilibrium. This paper develops a differentiable path-following method with a compact formulation to compute a proper equilibrium. The method incorporates square-root-barrier terms into payoff functions with an extra variable and constitutes a square-root-barrier game. As a result of this barrier game, we acquire a smooth path to a proper equilibrium. To further reduce the computational burden, we present a compact formulation of an ε-proper equilibrium with a polynomial number of variables and equations. Numerical results show that the differentiable path-following method is numerically stable and efficient. Moreover, by relaxing the requirements of proper equilibrium and imposing Selten's perfection, we come up with the notion of perfect d-proper equilibrium, which approximates a proper equilibrium and is less costly to compute. Numerical examples demonstrate that even when d is rather large, a perfect d-proper equilibrium remains to be a proper equilibrium. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms-Continuous. Funding: This work was partially supported by General Research Fund (GRF) CityU 11306821 of Hong Kong SAR Government. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0148) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0148). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

Software-as-a-service (SaaS) is gaining tremendous popularity in the enterprise software releases, which has brought the growing challenge for the incumbent used to adopt the on-premise licensing model. In this paper, we focus on the optimal versioning strategy problem of the incumbent when he faces the competition from the entrant who releases the SaaS software. He can choose from providing the upgraded on-premise software, turning to offer the SaaS version of the software, and releasing both the versions. We indicate that releasing both versions won't be the optimal choice in the competitive environment. When the upgrade cost is above a certain value, and the gap of value is below a threshold positively linear correlated with the upgrade cost, the incumbent prefers the SaaS strategy. Otherwise, the on-premise strategy generates the highest profit. A special case is that in the medium switching cost environment, the SaaS strategy can be optimal for all possible values of upgrade cost. Finally, We consider the problem in the presence of network effect and in the uncovered market setting. The results provide effective managerial insights into the strategy selection for the incumbent. [ABSTRACT FROM AUTHOR]

The subgame perfect equilibrium in stationary strategies (SSPE) is the most important solution concept in applications of stochastic games, making it imperative to develop efficient methods to compute an SSPE. For this purpose, this paper develops an interior-point differentiable path-following method (IPM), which establishes a connection between an artificial logarithmic barrier game and the stochastic game of interest by adding a homotopy variable. IPM brings several advantages over the existing methods for stochastic games. On the one hand, IPM provides a bridge between differentiable path-following methods and interior-point methods and remedies several issues of an existing homotopy method called the stochastic linear tracing procedure (SLTP). First, the starting stationary strategy profile can be arbitrarily chosen. Second, IPM does not need switching between different systems of equations. Third, the use of a perturbation term makes IPM applicable to all stochastic games rather than generic games only. Moreover, a well-chosen transformation of variables reduces the number of equations and variables by roughly one half. Numerical results show that the proposed method is more than three times as efficient as SLTP. On the other hand, the stochastic game can be reformulated as a mixed complementarity problem and solved by the PATH solver. We employ the proposed IPM and the PATH solver to compute SSPEs. Numerical results evince that for some stochastic games the PATH solver may fail to find an SSPE, whereas IPM is successful in doing so for all stochastic games, which confirms the reliability and stability of the proposed method. Summary of Contribution: This paper incorporates the interior-point methods into a differentiable path-following method for computing stationary equilibria for stochastic games. This novel method brings excellent computational advantages and remedies several issues with the existing methods for stochastic games. We prove the global convergence of the proposed method and employ this method to solve numerous randomly generated stochastic games with different scales. Numerical results further confirm the high efficiency, stability, and universality of this method for stochastic games. [ABSTRACT FROM AUTHOR]

Distance metric learning, which aims at learning an appropriate metric from data automatically, plays a crucial role in the fields of pattern recognition and information retrieval. A tremendous amount of work has been devoted to metric learning in recent years, but much of the work is basically designed for training a linear and global metric with labeled samples. When data are represented with multimodal and high-dimensional features and only limited supervision information is available, these approaches are inevitably confronted with a series of critical problems: 1) naive concatenation of feature vectors can cause the curse of dimensionality in learning metrics and 2) ignorance of utilizing massive unlabeled data may lead to overfitting. To mitigate this deficiency, we develop a semisupervised Laplace-regularized multimodal metric-learning method in this work, which explores a joint formulation of multiple metrics as well as weights for learning appropriate distances: 1) it learns a global optimal distance metric on each feature space and 2) it searches the optimal combination weights of multiple features. Experimental results demonstrate both the effectiveness and efficiency of our method on retrieval and classification tasks. [ABSTRACT FROM AUTHOR]

The two-cardinality sparse constrained optimization problems include sparse optimization problems and constrained sparse optimization problems in many fields, such as signal processing, image processing, securities investment etc. A smoothing penalty function method and a smoothing objective penalty function method are studied for two-cardinality sparse constrained optimization problems respectively. Some error estimations are proved for the smoothing penalty function and the smoothing objective penalty function. Based on the smoothing penalty function and smoothing objective penalty function, two algorithms are designed to solve two-cardinality sparse constrained optimization problems and their convergence is proved respectively. Numerical results show that the two algorithms have the similar effectiveness in finding out an approximate solution for two-cardinality sparse constrained optimization problems. [ABSTRACT FROM AUTHOR]

Purpose: With the rapid development of cloud computing, most software firms face the significant choice of whether they should change the versioning strategy of enterprise software from releasing the on-premise version to the software-as-a-service (SaaS) version. Data being generated and hosted on SaaS vendors' servers brings multiple effects. It enables customers to enjoy the flexibility of accessing data and using the software remotely, named the "portability" effect. However, on the other hand, the cumulative data resources on the cloud also provide a clear target for external attacks, leading to the concern of information security. Considering these, the authors hope to offer insights for software firms by exploring the strategy selection problem. Design/methodology/approach: Taking the portability effect and security risks of the SaaS licensing model into account, the authors develop a two-period model to figure out the market segmentation and identify the feasible conditions for employing three alternative strategies. Comparative statics analyses are conducted to explore the influencing mechanism of exogenous factors on strategy selection. The authors also discuss the strategy selection in the presence of the network effect and the security loss faced by users of on-premise software. Findings: One significant finding is that the on-premise strategy can be excluded when the potential loss from security risks is small. Under this circumstance, the dual version strategy is optimal provided that the increase of customer valuation caused by portability effect is below a threshold. Otherwise, the SaaS strategy generates the highest profit. When the potential loss from security risks turns large, the on-premise strategy, the dual version strategy and the SaaS strategy are the optimal options in order as the portability effect on customer valuation gets stronger. Originality/value: Previous literature has insufficiently addressed the versioning issue of enterprise software. In this paper, the distinctive features of the SaaS model are considered, and differentiated results compared with previous work are obtained. The research results provide guidelines for software firms in deciding their product releases in the future. [ABSTRACT FROM AUTHOR]

To extend the concept of subgame perfect equilibrium to an extensive-form game with imperfect information but perfect recall, Selten (Int J Game Theory 4:25–55, 1975) formulated the notion of perfect equilibrium and attained its existence through the agent normal-form representation of the extensive-form game. As a strict refinement of Nash equilibrium, a perfect equilibrium always yields a sequential equilibrium. The selection of a perfect equilibrium thus plays an essential role in the applications of game theory. Moreover, a different procedure may select a different perfect equilibrium. The existence of Nash equilibrium was proved by Nash (Ann Math 54:289–295, 1951) through the construction of an elegant continuous mapping and an application of Brouwer's fixed point theorem. This paper intends to enhance Nash's mapping to select a perfect equilibrium. By incorporating the complementarity condition into the equilibrium system with Nash's mapping through an artificial game, we successfully eliminate the nonnegativity constraints on a mixed strategy profile imposed by Nash's mapping. In the artificial game, each player solves against a given mixed strategy profile a strictly convex quadratic optimization problem. This enhancement enables us to derive differentiable homotopy systems from Nash's mapping and establish the existence of smooth paths for selecting a perfect equilibrium. The homotopy methods start from an arbitrary totally mixed strategy profile and numerically trace the smooth paths to a perfect equilibrium. Numerical results show that the methods are numerically stable and computationally efficient in search of a perfect equilibrium and outperform the existing differentiable homotopy method. [ABSTRACT FROM AUTHOR]

In most of the existing metric learning methods, the relation is fixed throughout the metric learning process. However, the fixed relation may be harmful to learn a good metric. The adversarial metric learning implements a dynamic update of the pairwise constraints. Inspired by the idea of dynamically updating constraints, we propose in this paper a metric learning model with clustering-based constraints (ML-CC), wherein the triple constraints of large margin are iteratively generated with the clusters of data points. The proposed method can overcome the shortage of the fixed triple constraints constructed under the Euclidian distance. The experimental results on synthetic and real datasets indicate that the performance of the ML-CC is superior to that of the existing state-of-the-art metric learning methods. [ABSTRACT FROM AUTHOR]

In the general equilibrium with incomplete asset markets (GEI) model, the excess demand functions are typically not continuous at the prices for which the assets have redundant returns. The reason is that, at these prices, the return matrix drops rank and households' budget sets collapse suddenly. This discontinuity results in a serious problem for the existence and computation of general equilibrium. In this paper, we show that this problem can be resolved with a new return matrix, which has constant rank. As a function of the price vector, the continuity of this new return matrix is ensured on a subset of the price space. This enables us to handle incomplete markets using a standard homotopy path-following argument by restricting the price vector to such a subset. The proposed approach naturally provides a constructive proof for the generic existence of general equilibrium. A homotopy method can then be applied to compute equilibria in the GEI model. Numerical experiments are presented to illustrate its efficiency. [ABSTRACT FROM AUTHOR]

Biconvex programming is nonconvex optimization describing many practical problems. The existing research shows that the difficulty in solving biconvex programming makes it a very valuable subject to find new theories and solution methods. This paper first obtains two important theoretical results about partial optimum of biconvex programming by the objective penalty function. One result holds that the partial Karush–Kuhn–Tucker (KKT) condition is equivalent to the partially exactness for the objective penalty function of biconvex programming. Another result holds that the partial stability condition is equivalent to the partially exactness for the objective penalty function of biconvex programming. These results provide a guarantee for the convergence of algorithms for solving a partial optimum of biconvex programming. Then, based on the objective penalty function, three algorithms are presented for finding an approximate ϵ -solution to partial optimum of biconvex programming, and their convergence is also proved. Finally, numerical experiments show that an ϵ -feasible solution is obtained by the proposed algorithm. [ABSTRACT FROM AUTHOR]

To manage the risk arising from uncertainty in market demand, this paper introduces the Conditional Value-at-Risk (CVaR) measure into the decision framework of the newsvendor who aims to minimise his opportunity loss. It is found under the CVaR measure that the newsvendor’s optimal order quantity is increasing in the confidence level when the understock loss is bigger than the overstock loss. This implies that an over-ordering may be even more caused by the newsvendor’s risk aversion about opportunity loss than risk seeking behaviour. Under this optimal order quantity, it is proved that the newsvendor’s expected profit and expected opportunity loss are decreasing and increasing in the confidence level, respectively. Furthermore, some management insights are presented to facilitate the risk management of the newsvendor model. [ABSTRACT FROM PUBLISHER]

Link prediction has received a great deal of attention from researchers. Most of the existing researches are based on the network topology but ignore the importance of its preference; for aggregating multiple pieces of information, they normally sum up them directly. In this paper, a path-based probabilistic model is proposed to estimate the potential connectivity between any two nodes. It takes carefully the effective influence of nodes and the dependency among paths between two fixed nodes into account. Furthermore, we formulate the connectivity of two inner-community nodes and that of two inter-community nodes. The qualitative analysis shows that the links between inner-community nodes are more likely to be predicted by the proposed model. The performance is verified on both the multi-barbell network and Lesmis network. Considering the proposed model's practicability, we develop an algorithm that iterates over the adjacent matrix to simulate paths of different lengths, with the parameters automatically grid-searched. The results of the experiments show that the proposed model outperforms competitive methods. [ABSTRACT FROM AUTHOR]

In this paper, a new alternating direction trust region method based on conic model is used to solve unconstrained optimization problems. By use of the alternating direction search method, the new conic model trust region subproblem is solved by two steps in two orthogonal directions. This new idea overcomes the shortcomings of conic model subproblem which is difficult to solve. Then the global convergence of the method under some reasonable conditions is established. Numerical experiment shows that this method may be better than the dogleg method to solve the subproblem, especially for large-scale problems. [ABSTRACT FROM AUTHOR]

This paper is concerned with the computation of equilibrium for an exchange economy with constant returns production technologies. We convert such an economy into a pure exchange economy by allocating the production to each consumer's endowment evenly. In this way, the market clearing condition of the original economy is reformulated as that of a pure exchange economy, together with an additional complementarity condition to ensure the feasibility of production plans. A homotopy method is proposed to solve these two problems simultaneously. With this approach, the economic equilibrium model with constant returns production can be handled in a similar way to the pure exchange economy. A path-following algorithm is then developed for computing equilibria in these economies. [ABSTRACT FROM AUTHOR]

The notion of perfect equilibrium was formulated by Selten (Int J Game Theory 4(1):25–55, 1975) as a strict refinement of Nash equilibrium. For an extensive-form game with perfect recall, every perfect equilibrium of its agent normal-form game yields a perfect equilibrium of the extensive-form game. This paper aims to develop a differentiable homotopy method for computing perfect equilibria of normal-form games. To accomplish this objective, we constitute an artificial game by introducing a continuously differentiable function of an extra variable. The artificial game defines a differentiable homotopy mapping and establishes the existence of a smooth path to a perfect equilibrium. For numerical comparison, we also describe a simplicial homotopy method. Numerical results show that the differentiable homotopy method is numerically stable and efficient and significantly outperforms the simplicial homotopy method especially when the problem is large. [ABSTRACT FROM AUTHOR]

The computation of subgame perfect equilibrium in stationary strategies is an important but challenging problem in applications of stochastic games. In 2004, Herings and Peeters developed a homotopy method called stochastic linear tracing procedure to solve this problem. However, the starting point of their method requires to be explicitly calculated. To remedy this issue, we formulate an arbitrary starting linear tracing procedure in this paper. By introducing a homotopy variable ranging from two to zero, an artificial penalty game is developed, whose solutions construct a differentiable path after a well-chosen transformation of variables. The starting point of the path can be arbitrarily chosen, so that there is no need to employ additional algorithms to obtain it. Following the path, one can readily attain the "starting point" of the stochastic tracing procedure coined by Herings and Peeters. Then, as the homotopy variable changes from one to zero, the path essentially resumes to the stochastic tracing procedure. We prove that our method globally converges to a subgame perfect equilibrium in stationary strategies for the stochastic game of interest. Numerical results further illustrate the effectiveness and efficiency of our method. [ABSTRACT FROM AUTHOR]

This article presents a non-expected utility decision model which is nonlinear in the winning probabilities. The model not only explicitly expresses bidders' attitudes to risk, but also addresses their preference over the bidding criteria. To demonstrate how to apply the model in the practical auction design, the first- and second-price auctions with both commission rate and reserve price are examined, respectively. For nonrisk-neutral bidders, the equilibrium bidding strategies are characterized, in which the commission rate has a significant influence on the bidding strategy through the critical valuation. However, the existence of the optimal commission rate is uncertain, but once it exists, it depends on the information rent of the highest or second highest order valuation in terms of the inverse hazard rate. With risk-aversion bidders, the only difference to the optimal reserve price is a constant between the first- and second-price auctions. The revenue comparisons show that the classical Revenue Equivalence Theorem fails in practical auctions with the commission rate. This article extends the application of the decision-making model in the auction design in theory and provides some guidance for the auction house and the seller to make their decisions in reality. [ABSTRACT FROM AUTHOR]

This paper is concerned with the computation of perfect stationary point, which is a strict refinement of stationary point. A differentiable homotopy method is developed for finding perfect stationary points of continuous functions on convex polytopes. We constitute an artificial problem by introducing a continuously differentiable function of an extra variable. With the optimality conditions of this problem and a fixed point argument, a differentiable homotopy mapping is constructed. As the extra variable becomes close to zero, the homotopy path naturally provides a sequence of closely approximate stationary points on perturbed polytopes, and converges to a perfect stationary point on the original polytope. Numerical experiments are implemented to further illustrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

In the domain of Home Health Care (HHC), precise decisions regarding patient's selection, staffing level, and scheduling of health care staff have a significant impact on the efficiency and effectiveness of the HHC system. However, decentralized planning, the absence of well defined decision rules, delayed decisions and lack of interactive tools typically lead towards low satisfaction level among all the stakeholders of the HHC system. In order to address these issues, we propose an integrated three phase decision support methodology for the HHC system. More specifically, the proposed methodology exploits the structure of the HHC problem and logistic regression based approaches to identify the decision rules for patient acceptance, staff hiring, and staff utilization. In the first phase, a mathematical model is constructed for the HHC scheduling and routing problem using Mixed-Integer Linear Programming (MILP). The mathematical model is solved with the MILP solver CPLEX and a Variable Neighbourhood Search (VNS) based method is used to find the heuristic solution for the HHC problem. The model considers the planning concerns related to compatibility, time restrictions, distance, and cost. In the second phase, Bender's method and Receiver Operating Characteristic (ROC) curves are implemented to identify the thresholds based on the CPLEX and VNS solution. While the third phase creates a fresh solution for the HHC problem with a new data set and validates the thresholds predicted in the second phase. The effectiveness of these thresholds is evaluated by utilizing performance measures of the widely-used confusion matrix. The evaluation of the thresholds shows that the ROC curves based thresholds of the first two parameters achieved 67% to 71% accuracy against the two considered solution methods. While the Bender's method based thresholds for the same parameters attained more than 70% accuracy in cases where probability value is small (p ≤ 0.5). The promising results indicate that the proposed methodology is applicable to define the decision rules for the HHC problem and beneficial to all the concerned stakeholders in making relevant decisions. [ABSTRACT FROM AUTHOR]

Micro surface modeling has been widely applied in micro scale systems, and the advanced modeling of micro surface is crucial to the development of micro scale systems. In this study, based on 3 subdivision schemes, an improved uniform micro subdivision algorithm is proposed for micro surface modeling. The original 3 subdivision scheme could not accommodate the sharp features on the micro surface in determining the micro local property of the surface. However, the proposed improved subdivision algorithm can overcome this difficulty without changing the topology of the subdivision surface. The proposed algorithm uses an interpolation subdivision method and obtains excellent results by preserving the dart, crease, corner, and cone. The micro subdivision surface can reach everywhere smoothly except for some infinite sharp features. The proposed algorithm can also deal with nano models, such as micro robots, nano artificial modeling, and micro 3D characters. The experimental results demonstrate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

As a strict refinement of Nash equilibrium, the concept of perfect equilibrium was formulated by Selten (Int J Game Theory 4(1):25–55, 1975). A well-known application of this concept is that every perfect equilibrium of the agent normal form game of an extensive form game with perfect recall yields a trembling-hand perfect equilibrium (consequently a sequential equilibrium). To compute a perfect equilibrium, this paper extends Kohlberg and Mertens's equivalent reformulation of Nash equilibrium to a perturbed game. This extension naturally leads to a homotopy mapping on the Euclidean space. With this homotopy mapping and a triangulation, we develop a simplicial homotopy method for approximating perfect equilibria. It is proved that every limit point of the simplicial path yields a perfect equilibrium. Numerical results further confirm the effectiveness of the method. [ABSTRACT FROM AUTHOR]

In many real-world classification problems, accurate prediction of membership probabilities is critical for further decision making. The probability calibration problem studies how to map scores obtained from one classification algorithm to membership probabilities. The requirement of non-decreasingness for this mapping involves an infinite number of inequality constraints, which makes its estimation computationally intractable. For the sake of this difficulty, existing methods failed to achieve four desiderata of probability calibration: universal flexibility, non-decreasingness, continuousness and computational tractability. This paper proposes a method with shape-restricted polynomial regression, which satisfies all four desiderata. In the method, the calibrating function is approximated with monotone polynomials, and the continuously-constrained requirement of monotonicity is equivalent to some semidefinite constraints. Thus, the calibration problem can be solved with tractable semidefinite programs. This estimator is both strongly and weakly universally consistent under a trivial condition. Experimental results on both artificial and real data sets clearly show that the method can greatly improve calibrating performance in terms of reliability-curve related measures. [ABSTRACT FROM AUTHOR]

This article introduces a smoothing technique to the l1 exact penalty function. An application of the technique yields a twice continuously differentiable penalty function and a smoothed penalty problem. Under some mild conditions, the optimal solution to the smoothed penalty problem becomes an approximate optimal solution to the original constrained optimization problem. Based on the smoothed penalty problem, we propose an algorithm to solve the constrained optimization problem. Every limit point of the sequence generated by the algorithm is an optimal solution. Several numerical examples are presented to illustrate the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a smooth path-following algorithm for computing market equilibrium in a pure exchange economy under a class of piecewise-smooth concave utilities, which can be expressed as u(x)=minℓ{fℓ(x)} with fℓ(x) being a smooth concave function for all ℓ. As a result of a smooth technique for minimax problems, a smooth homotopy mapping is derived from the introduction of logarithmic barrier terms and an extra variable. With this mapping, it is proved that there always exists a smooth path leading to a market equilibrium as the extra variable approaches zero. A predictor-corrector method is adapted for numerically following this path. Numerical results are given to further demonstrate the effectiveness and efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

Maybe it is the most important medical reform for current China to adopt the bid-and-procurement scheme to correct the distortion of pharmaceutical resources allocation. Nevertheless, overpriced drugs often happen. This article aims to identify potential factors leading to the overpriced. Based on the mechanism rules of the scheme, it is found that unethical doctors are crucial to high price markup in the pricing pattern of drugs. Under China's actual conditions, asymmetric ownership is identified to be another cause of the overpriced by developing an asymmetric bidding model. How are the impacts of these two factors to be alleviated? Upon examination, several reform measures cannot effectively avoid the occurrence of the overpriced. Yet, the issue is very urgent for China because it is facing with the problem of population aging. Therefore, alternative options - a regulation-penalty tool and an investment subsidy policy - are proposed to improve China's health care. [ABSTRACT FROM AUTHOR]

Development of an efficient and effective home health care (HHC) service system is a quite recent and challenging task for the HHC firms. This paper aims to develop an HHC service system in the perspective of long-term economic sustainability as well as operational efficiency. A more flexible mixed-integer linear programming (MILP) model is formulated by incorporating the dynamic arrival and departure of patients along with the selection of new patients and nursing staff. An integrated model is proposed that jointly addresses: (i) patient selection; (ii) nurse hiring; (iii) nurse to patient assignment; and (iv) scheduling and routing decisions in a daily HHC planning problem. The proposed model extends the HHC problem from conventional scheduling and routing issues to demand and capacity management aspects. It enables an HHC firm to solve the daily scheduling and routing problem considering existing patients and nursing staff in combination with the simultaneous selection of new patients and nurses, and optimizing the existing routes by including new patients and nurses. The model considers planning issues related to compatibility, time restrictions, contract durations, idle time and workload balance. Two heuristic methods are proposed to solve the model by exploiting the variable neighborhood search (VNS) approach. Results obtained from the heuristic methods are compared with a CPLEX based solution. Numerical experiments performed on different data sets, show the efficiency and effectiveness of the solution methods to handle the considered problem. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm of barrier objective penalty function for inequality constrained optimization is studied and a conception–the stability of barrier objective penalty function is presented. It is proved that an approximate optimal solution may be obtained by solving a barrier objective penalty function for inequality constrained optimization problem when the barrier objective penalty function is stable. Under some conditions, the stability of barrier objective penalty function is proved for convex programming. Specially, the logarithmic barrier function of convex programming is stable. Based on the barrier objective penalty function, an algorithm is developed for finding an approximate optimal solution to an inequality constrained optimization problem and its convergence is also proved under some conditions. Finally, numerical experiments show that the barrier objective penalty function algorithm has better convergence than the classical barrier function algorithm. [ABSTRACT FROM PUBLISHER]

This paper is concerned with theH∞filtering problem for a class of continuous-time linear switched systems with the asynchronous behaviours, where ‘asynchronous’ means that the switching of the filters to be designed has a lag to the switching of the system modes. By using the Lyapunov-like functions and the average dwell time technique, a sufficient condition is obtained to guarantee the asymptotic stability with a weightedH∞performance index for the filtering error system. Moreover, the results are formulated in the form of linear matrix inequalities that are numerical feasible. As a result, the filter design problem is solved. Finally, an illustrative numerical example is presented to show the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This paper considers $$H_{\infty }$$ filtering of discrete-time uncertain switched nonlinear systems with time-varying delay via Takagi-Sugeno fuzzy model which is used to approximate each nonlinear subsystem. Fuzzy piecewise Lyapunov-Krasovskii functionals and average dwell time approaches are utilized for the exponential stability analysis and $$H_{\infty }$$ filter design. A new sufficient condition is obtained to guarantee the exponential stability with a prescribed $$H_{\infty }$$ performance index for the filtering error system. Filter parameter matrices can be obtained by solving sets of linear matrix inequalities. An example of an uncertain single-link robot arm is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A fuzzy granular structure refers to a mathematical structure of the collection of fuzzy information granules granulated from a dataset, while a fuzzy information granularity is used to measure its uncertainty. However, the existing forms of fuzzy information granularity have two limitations. One is that when the fuzzy information granularity of one fuzzy granular structure equals that of the other, one can say that these two fuzzy granular structures possess the same uncertainty, but these two fuzzy granular structures may be not equivalent to each other. The other limitation is that existing axiomatic approaches to fuzzy information granularity are still not complete, under which when the partial order relation among fuzzy granular structures cannot be found, their coarseness/fineness relationships will not be revealed. To address these issues, a so-called fuzzy granular structure distance is proposed in this study, which can well discriminate the difference between any two fuzzy granular structures. Besides this advantage, the fuzzy granular structure distance has another important benefit: It can be used to establish a generalized axiomatic constraint for fuzzy information granularity. By using the axiomatic constraint, the coarseness/fineness of any two fuzzy granular structures can be distinguished. In addition, through taking the fuzzy granular structure distances of a fuzzy granular structure to the finest one and the coarsest one into account, we also can build a bridge between fuzzy information granularity and fuzzy information entropy. The applicable analysis on 12 real-world datasets shows that the fuzzy granular structure distance and the generalized fuzzy information granularity have much better performance than existing methods. [ABSTRACT FROM AUTHOR]

Augmented Lagrangian function is one of the most important tools used in solving some constrained optimization problems. In this article, we study an augmented Lagrangian objective penalty function and a modified augmented Lagrangian objective penalty function for inequality constrained optimization problems. First, we prove the dual properties of the augmented Lagrangian objective penalty function, which are at least as good as the traditional Lagrangian function's. Under some conditions, the saddle point of the augmented Lagrangian objective penalty function satisfies the first-order Karush-Kuhn-Tucker condition. This is especially so when the Karush-Kuhn-Tucker condition holds for convex programming of its saddle point existence. Second, we prove the dual properties of the modified augmented Lagrangian objective penalty function. For a global optimal solution, when the exactness of the modified augmented Lagrangian objective penalty function holds, its saddle point exists. The sufficient and necessary stability conditions used to determine whether the modified augmented Lagrangian objective penalty function is exact for a global solution is proved. Based on the modified augmented Lagrangian objective penalty function, an algorithm is developed to find a global solution to an inequality constrained optimization problem, and its global convergence is also proved under some conditions. Furthermore, the sufficient and necessary calmness condition on the exactness of the modified augmented Lagrangian objective penalty function is proved for a local solution. An algorithm is presented in finding a local solution, with its convergence proved under some conditions. [ABSTRACT FROM PUBLISHER]

Integer programming is concerned with the determination of an integer or mixed-integer point in a polytope. It is an NP-hard problem and has many applications in economics and management. Although several popular methods have been developed for integer programming in the literature and extensively utilized in practices, it remains a challenging problem and appeals for more endeavors. By constructing an increasing mapping satisfying certain properties, we develop in this paper an alternative method for integer programming, which is called a fixed point iterative method. Given a polytope, the method, within a finite number of iterations, either yields an integer or mixed-integer point in the polytope or proves no such point exists. As a very appealing feature, the method can easily be implemented in a distributed way. Furthermore, the construction implies that determining the uniqueness of Tarski's fixed point is an NP-hard problem, and the method can be applied to compute all integer or mixed-integer points in a polytope and directly extended to convex nonlinear integer programming. Preliminary numerical results show that the method seems promising. [ABSTRACT FROM AUTHOR]

Decision makers often express their evaluations on decision problems with multi-granular linguistic terms. This fact leads to the unification of the multi-granular linguistic terms into a single linguistic set in the literature. However, this unification process increases the complexity of computation and the subjectivity in the determination of transformation functions. To overcome this deficiency, this paper aims to develop a normalized numerical scaling method for determining the semantics of multi-granular linguistic terms in the same domain. We first introduce a class of numerical scaling functions to generate several balanced or unbalanced linguistic sets. Since these scaled linguistic sets have different domains, we then develop a normalized numerical scaling method to form them into the unique interval [0,1]. As a result of this development, two classes of normalized scaling functions are derived from the priori scale information and applications of piecewise linear interpolation and piecewise arc interpolation. Finally, an example is given to illustrate how the method works. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability and L2-gain problems for a class of continuous-time linear switched systems with the existed asynchronous behaviors, where 'asynchronous' means that the switching of the controllers to be designed has a lag to the switching of the system modes. Firstly, a new sufficient condition on the asymptotic stability and weighted L2-gain analysis is obtained by using multiple Lyapunov functions combined with the average dwell time technique. Moreover, a result that is formulated in form of linear matrix inequalities is derived for the problem of asynchronous H ∞ control. Based on the result, the mode-dependent controllers can be designed. Finally, an illustrative numerical example is presented to show the effectiveness of the obtained results.Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability analysis and H∞ fuzzy controller design of continuous-time fuzzy interconnected systems with time-varying delays. The fuzzy interconnected system consists of N interconnected time-delay Takagi-Sugeno(T-S) fuzzy subsystems and the delay-dependent stability analysis is based on the fuzzy weighting-dependent Lyapunov-Krasovskii functionals. It is shown that the delay-dependent stability of the time-delay fuzzy interconnected systems can be established if a fuzzy weighting-dependent Lyapunov-Krasovskii functional can be constructed, and moreover, the functional can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. The decentralized H∞ controllers are also designed by solving a set of LMIs based on these fuzzy weighting-dependent Lyapunov-Krasovskii functionals. It is demonstrated via numerical examples that the stability and controller synthesis results based on fuzzy weighting-dependent Lyapunov-Krasovskii functionals are less conservative than those based on the common quadratic Lyapunov-Krasovskii functionals. [ABSTRACT FROM AUTHOR]

Many real data increase dynamically in size. This phenomenon occurs in several fields including economics, population studies, and medical research. As an effective and efficient mechanism to deal with such data, incremental technique has been proposed in the literature and attracted much attention, which stimulates the result in this paper. When a group of objects are added to a decision table, we first introduce incremental mechanisms for three representative information entropies and then develop a group incremental rough feature selection algorithm based on information entropy. When multiple objects are added to a decision table, the algorithm aims to find the new feature subset in a much shorter time. Experiments have been carried out on eight UCI data sets and the experimental results show that the algorithm is effective and efficient. [ABSTRACT FROM AUTHOR]