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The article discusses the result of an experimental study which shows that people do not follow the optimal strategy in practice and suggests two strategies for defeating human opponents in rock-paper-scissors (RPS). The study found that the probability of repeating a game on the next trial is well above one-third, while the strategy of always playing the symbol is assessed to be an effective strategy in defeating the symbol that the other player has previously played. The study also observed that the wins of each competition have increased by 26.4%, while the losses are decreased by 9.51%.

A non-smooth biobjective optimization problem for designing the shape of a slice channel in a paper machine headbox is described. The conflicting goals defining the optimization problem are the ones determining important quality properties of produced paper: 1) basis weight should be even and 2) the wood fibers of paper should mainly be oriented to the machine direction across the width of the whole paper machine. The novelty of the considered approach is that maximum deviations are used instead of least squares when objective functions are formed. For the solution of this problem, a multiobjective genetic algorithm based on nondominated sorting is considered. The numerical results demonstrate the ability to obtain a large set of nondominated designs. [ABSTRACT FROM AUTHOR]

With this note, we want to open a discussion on the duality theory for Interval Optimization. We begin by showing that some duality results Wu ( J Optim Theory Appl 144:615-628, ) are useless. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we determine the modularities of asymptotically optimal towers found by Maharaj and Wulftange in 2005. This is also a continuation of the work of Elkies in 2002. [Copyright &y& Elsevier]

Abstract: A generalization of two sharp inequalities in a recent paper by N. Ujević is established. Applications in numerical integration are also given and the results of N. Ujević are revised and improved. [Copyright &y& Elsevier]

Abstract: The aim of this note is to show that the optimization algorithm proposed in may not lead to the optimal solution in some cases. In fact, the optimization problem remains open if we do not apply the branch-and-bound method to solve it or compute all the objective values of minimal solutions of the feasible domain. [Copyright &y& Elsevier]

Abstract: A counterexample is provided in this short note to show that some of local convergence theorems established in [D.K.R. Babajee, M.Z. Dauhoo, An analysis of the properties of the variants of Newton’s method with third order convergence, Appl. Math. Comput. 183 (2006) 659–684] are not always true. Some mistakes in the proofs of these theorems are pointed out. [Copyright &y& Elsevier]

This article provides instructions in preparing a paper for publication in the "Journal of Optimization Theory and Applications." Some of these guidelines are the following: 1)submission of manuscripts in triplicate; 2) reference to English as the official language of the journal; 3) inclusion of an abstract of at least 50 to 100 words in each contribution; and, 4) the abstract should be followed by a list of four to five key words identifying the subject.

Presents manuscript guidelines for papers to be published in the "Journal of Optimization Theory and Applications."

Abstract  In this paper, a filled function method for solving constrained global optimization problems is proposed. A filled function is proposed for escaping the current local minimizer of a constrained global optimization problem by combining the idea of filled function in unconstrained global optimization and the idea of penalty function in constrained optimization. Then a filled function method for obtaining a global minimizer or an approximate global minimizer of the constrained global optimization problem is presented. Some numerical results demonstrate the efficiency of this global optimization method for solving constrained global optimization problems. [ABSTRACT FROM AUTHOR]

The article discusses the 2005 best paper awardee of the Computational Optimization and Applications entitled "Hyper-Sparsity in the Revised Simplex Method and How to Exploit It," by Julian Hall and Ken McKinnon of the University of Edinburgh, Scotland. The continuity in the sparsity of the right -hand-side was initially denoted as super-sparsity. The authors observed that the same behaviour was detected when applying the basis matrix factors to the two linear systems that are solved in each process of the revised simple system. For linear programming problems that exhibit hyper-sparsity, the value of it will count on the performance of those elements.

Full factorial experimental design technique was used to study the main effects and interactions between operational parameters in batch adsorption of methylene blue (MB) using Alfa stems as adsorbent. The important parameters which affect MB removal efficiency and adsorption amount, such as initial concentration, particle size, solution pH, and contact time, were investigated. One set of full 24factorial designs with two central points (18 experiments) was tested. The effects of individual variables and their interactions were observed on adsorbed MB amountqt(mg/g). From statistical analysis, the most effective parameters of adsorbed MB amount were initial concentration and solution pH. The interaction between initial concentration and solution pH was the most important factor. The maximum quantity retained was 25.89 mg/g; it was obtained with an initial concentration of 100 mg/L, adsorbent dose of 4 g/L, granulometry of [0.50–0.63 mm], and pH of the solution 12, with a stirring velocity of 500 rpm for 120 min. [ABSTRACT FROM AUTHOR]

In this paper, using improvement-valued maps, we define two types of E-Benson proper efficient elements for subsets within a linear space under a variable ordering map C. Consequently, we delve into studying two types of E-Benson proper efficient solutions of vector optimization problems under variable ordering structures. We establish relationships among different types of E-Benson proper efficient elements. Furthermore, we demonstrate that the two types of E-Benson proper efficiency, in relation to the ordering map C, not only unify and extend certain notions of (weakly) nondominated elements but also extend some well-known notions of Benson proper efficiency under fixed ordering structures. Lastly, under suitable assumptions, we establish linear scalarization theorems for E-Benson proper efficient solutions of vector optimization problems under variable ordering structures. Several examples are also provided to illustrate the derived results. [ABSTRACT FROM AUTHOR]

The article presents a study that determines the effect of the structural error of biosphere models when used in assimilating net ecosystem exchange (NEE) measurements to optimize uncertain model parameters within carbon cycle data assimilation 5 systems (CCDASs). It describes the method of the research that observes data from the model-minus-observation mismatch statistics. It notes the result of the study, which confirms the inferred characteristics of the model.

Economic dispatch with valve-point effect (EDVPE) considered is presented as a more accurate model of the real problem compared to the conventional economic dispatch model. It is basically a non-convex, non-differentiable, and multi-modal optimization model with many local minima. Part I of the paper focuses on the local minimum analysis of the EDVPE. The analysis indicates that a local minimum consists of the singular points, the small convex regions, and the output of a slack unit that is dispatched to balance the load demand. Two types of local minima are identified and the second type could be ignored. To verify the rationality of the analyses, a traverse search has been performed to solve the EDVPE with and without considering the transmission loss on different test systems. All the simulation results support the analysis given in the paper. To effectively solve the EDVPE on a large-scale power system, based on the analysis presented in this paper, a new method, dimensional steepest decline method, is proposed in Part II of the paper. [ABSTRACT FROM PUBLISHER]

In the 1990s, the united nations development programme (UNDP) introduced the human development index (HDI) to determine the development degrees of countries. One deficiency in the HDI calculation is the use of equal weights for its sub-indicators. Many scholars have tried to solve this problem using a data envelopment analysis (DEA) method, particularly the one enhanced by weight restrictions. Indeed no specific method has been yet suggested to determine the parameters of the weight restrictions. In this paper, we use four DEA/benefit of the doubt (BoD) models enriched by the assurance regions type I (AR-I) constraints to assess human development; we aim to objectively determine the AR-I bounds. Therefore, we consider a basis as the accepted human development values and propose a bi-level optimization problem to extract the AR-I bounds in such a way that the efficiency scores are almost the same as the basic values. On the other hand, the HDI is a globally accepted index that shows small changes year by year. So, if the UNDP decides to apply a BoD model for calculating the HDI instead of the traditional method, then it is better than the scores obtained by the BoD model, showing small changes in comparison with the HDI, at least in the first few years. Therefore, the HDI values are considered as the basis. Moreover, the objectively achieved AR-I bounds provide us with an insight into the way the sub-indicators affect the development scores. The bounds can be modified by the experts opinions, in the future. [ABSTRACT FROM AUTHOR]

The objectives of this paper are to analyze different linear optimization models for the One-dimensional Cutting Stock Problem and, by using a fuzzy classification approach, determine the reutilization of the leftovers from the cutting process. The optimal solutions of the proposed linear models are obtained from Simplex Method. The fuzzy classification system is a collaborative decision-making tool, which analyzes uncertain parameters in the manufacturing process in order to determine, according to the given objective, the most appropriate cutting pattern, also classifying the results provided by different linear optimization models. The comparison of the results allows to infer the most appropriate model to use according to the specifications of the problem to be solved. Results are obtained from a case study, in a packaging company, located in the state of Paraná, Brazil, which aims to select the best cutting pattern for two different scenarios: one with concentration of leftovers on standardized objects, and the other on non-standardized objects. [ABSTRACT FROM AUTHOR]

A preface to a 2014 issue of the "Journal of Optimization Theory & Applications" is presented.

Introduces a series of articles which appeared in the January 2005 issue. Reference to the papers presented at the 5th International Conference on Optimization: Techniques and Applications in Hong Kong, China; Claim that the papers were divided into three categories which are nonlinear optimization, scheduling and discrete optimization and engineering optimization.

Puzzle-based storage systems consist of densely stored unit loads on a square grid. The problem addressed in this paper is to retrieve a stored unit load from a puzzle-based storage using the minimum number of item moves. While previous research contributed optimal algorithms for only up to two empty locations (escorts), our approach solves configurations where multiple empty locations are arbitrarily positioned in the grid. The problem is formulated as a state space problem and solved to optimality using an exact search algorithm. To reduce the search space, we derive bounds on the number of eligible empty locations and develop several search-guiding estimate functions. Furthermore, we present a heuristic variant of the search algorithm to solve larger problem instances. We evaluate both solution algorithms on a large set of problem instances. Our computational results show that the algorithms clearly outperform existing approaches where they are applicate and solve more general configurations, which could not be solved to optimality before. The heuristic variant efficiently yields high-quality solutions for significantly larger instances of practically relevant size. [ABSTRACT FROM AUTHOR]

This paper presents a piecewise convexification method with a box classification strategy to approximate the entire globally optimal solution set of non-convex optimization problems with box constraints. First, the box classification strategy is proposed based on the convexity of the objective function on the sub-boxes, which helps to reduce the number of box divisions and improve the computational efficiency. At the same time, we construct the piecewise convexification problem of the original non-convex optimization problem by applying the α-based Branch-and-Bound (a BB) method, and we define the (approximate) solution set of the piecewise convexification problem based on the result of classifying the sub-boxes. Then, it is deduced that the globally optimal solution set can be approximated by the (approximate) solution set of the piecewise convexification problem. Finally, a piecewise convexification algorithm is proposed that includes a new subset selection technique for division and two new termination tests. The results of our experiments demonstrate the effectiveness and general superiority of our approach over the competition. [ABSTRACT FROM AUTHOR]

Optimization problems relating to heat source operation are solved via linear (LP) or nonlinear (NLP) programming. The optimization methods used can be compared based on the complexity of the computational program setup, the time required to input and update data, and the computational time required for the optimal shifting and loading of installed power machinery. LP methods are preferred (e.g., the simplex method, the method of characteristics), but the Lagrange multiplier NPL method is sometimes applied. In this paper, the method of proportional increments (LP and NLP) is applied to compare the optimal loadings of power machinery installed in a thermal power plant using linear and quadratic economic characteristics. [ABSTRACT FROM AUTHOR]

The article provides general information related to the Journal of Optimization Theory and Application, as of August 1, 2003. The journal publishes carefully selected papers covering mathematical optimization techniques and their applications to science and engineering. Typical areas of application are, aerospace, mechanical engineering, mathematical biology, mathematical economics, and mathematical physics. The journal publishes survey papers, technical notes, book notices and other types of articles.

Product line planning (PLP) aims at an optimal combination of product feature offerings, suggesting itself to be a determinant decision for a company to satisfy diverse customer needs and gain competitive advantages. Fulfilment of planned product lines must make trade-offs between product variety and production costs. To balance the costs of product lines, manufacturers often adopt a product platform configuration (PPC) approach to redesign product and process platforms by adding new modules to the legacy platforms. The PPC is an effective means of providing product variety while controlling the manufacturing costs. The PLP and PPC problems have traditionally been investigated separately in the marketing research and engineering design fields. It is important to coordinate PLP and PPC decisions within a coherent optimisation framework. This paper proposes a bilevel mixed 0–1 nonlinear programming model to formulate coordinated optimisation for platform-driven product line planning. The upper level deals with the PLP problem by maximising the profit of an entire product line, whilst the lower level copes with the multiple product platforms optimisation for the optimal PPC in accordance with the upper level decisions of product line structure. To solve this bilevel programming model, a bilevel genetic algorithm is developed to find the optimal solution. A case study of coordinated optimisation between an automobile line and its product platforms is presented to demonstrate the feasibility and effectiveness of the proposed bilevel programming in comparison with a typical ‘all-in-one’ approach and a non-joint optimisation programming. [ABSTRACT FROM AUTHOR]

Compared with the conventional two-level dual-active-bridge (DAB) dc–dc converter, the three-level DAB converter could operate with lower voltage rated switching devices and provide more control degrees of freedom, which enhances the control flexibility. This paper proposes a modulation strategy with five control degrees of freedom. In the previous work with multiple control degrees, the optimization strategies for efficiency or inductor current minimization are investigated; however, these strategies all need detailed mode analysis and complex mathematical optimization tools to obtain the optimal duty cycles. In this paper, an optimization strategy for the root-mean-square value of the inductor current is proposed. This method extracts the fundamental and third-harmonic components from the high-frequency voltages on both sides and adjusts the amplitude of the bridge voltages by the vector diagram to obtain the optimal duty cycles. The inductor current can be reduced significantly at light loads with the proposed strategy, so the efficiency of the converter can be improved. Moreover, the optimization process does not need the detailed operation analysis of the converter, nor does it require the complex mathematical optimization tools. Finally, the performance of the three-level DAB and the optimization strategy are verified by the experimental results. [ABSTRACT FROM AUTHOR]

The optimization of functions to find the best solution according to one or several objectives has a central role in many engineering and research fields. Recently, a new family of optimization algorithms, named quality-diversity (QD) optimization, has been introduced, and contrasts with classic algorithms. Instead of searching for a single solution, QD algorithms are searching for a large collection of both diverse and high-performing solutions. The role of this collection is to cover the range of possible solution types as much as possible, and to contain the best solution for each type. The contribution of this paper is threefold. First, we present a unifying framework of QD optimization algorithms that covers the two main algorithms of this family (multidimensional archive of phenotypic elites and the novelty search with local competition), and that highlights the large variety of variants that can be investigated within this family. Second, we propose algorithms with a new selection mechanism for QD algorithms that outperforms all the algorithms tested in this paper. Lastly, we present a new collection management that overcomes the erosion issues observed when using unstructured collections. These three contributions are supported by extensive experimental comparisons of QD algorithms on three different experimental scenarios. [ABSTRACT FROM PUBLISHER]

A memetic algorithm based on MOEA/D is presented to deal with the uncapacitated multiobjective examination timetabling problem in this paper. The examination timetabling problem is considered as a two-objective optimization problem in this paper, while it is modeled as a single-objective optimization problem generally. The framework of a multiobjective evolutionary algorithm with decomposition (MOEA/D) is first employed to guide the evolutionary process. Two special local search operators are designed to find better individuals. The proposed algorithm is tested on 11 benchmark examination timetabling instances. Experimental results prove that the proposed algorithm can produce a promising set of nondominated solutions for each examination timetabling instance. [ABSTRACT FROM AUTHOR]

The article presents a preface for the conference papers are being submitted to the conference on Variational Analysis and Optimization held on 18 May to 22 May 2015 in Limoges, France.

This document is a preface to a special issue of the Serdica Mathematical Journal dedicated to the memory of Asen Lyubomirov Dontchev, a renowned mathematician who specialized in variational analysis, optimization, and optimal control. Dontchev passed away in 2021 at the age of 73. The preface provides a brief overview of Dontchev's career, including his education, research contributions, and publications. It also mentions his role as a mentor and his involvement in various mathematical journals. The special issue contains papers written by Dontchev's colleagues, friends, former students, and collaborators as a tribute to his work and influence. [Extracted from the article]

A preface for the special issue of "Journal of Global Optimization" featuring papers selected from the 8th International Conference on Optimization: Techniques and Applications held in Shanghai, China is presented.

In this paper, we consider a projected gradient method for constrained multiobjective optimization problems. Under suitable assumptions, we show that the sequence generated by the method converges to a Pareto stationary point (or a weak Pareto optimal point) of the problem when the multiobjective function is quasiconvex (or pseudoconvex). Furthermore, in the case that the multiobjective function is convex, by using some approximate conditions that are imposed on the gradients of the objective functions and the search directions, we obtain the linear convergence result for this method. [ABSTRACT FROM AUTHOR]

Medical staff configuration is a critical problem in the management of an emergency department (ED) in Hong Kong (HK). Given the service requirements by HK government, it is imperative for the hospital managers to develop medical staff configuration in a cost-and-time-effective way. In this paper, the medical staff configuration problem in ED is modeled as minimizing the total labor cost while satisfying the service quality requirements. To solve this issue, we propose a highly efficient search method, called random boundary generation with feasibility detection (RBG-FD). The random boundary generation (RBG) is applied to efficiently identify good-quality solutions based on the objective value. The feasibility detection (FD) procedure is used to retain the probability of correct feasibility detection of each sampled solution at the desired level, which intrinsically allocates a reasonable number of simulation replications. To estimate the performance measures of the ED, a discrete-event simulation model is developed to reflect the patient flow. Using these techniques, the efficiency of identifying the optimal staff configuration can be significantly improved. A case study is performed in a public hospital in HK. The numerical results indicate significantly higher practicability and efficiency of the proposed method with different patient arrival rates and service constraints. Note to Practitioners This paper seeks to solve the problem of minimizing the medical staff cost constrained by certain service requirements [i.e., patients’ waiting times for treatment] at an emergency department in Hong Kong. In our formulation, these service requirements are characterized by some stochastic constraints. Most of the existing random search methods concentrate on the computing efforts in the neighborhood of the best-so-far solutions in order to obtain good-quality solutions. Due to the special structure of this problem and ease of computing the objective values, we proposed an efficient random search approach that iteratively identifies a solution with a better objective value than that of the current best solution. Experimental studies demonstrate the significantly higher efficiency of this method. In order to obtain the same solution quality, it is able to reduce the computational time by 90% compared with some existing approaches in the literature. [ABSTRACT FROM PUBLISHER]

This paper studies $$\varepsilon $$ -efficiency in multiobjective optimization by using the so-called coradiant sets. Motivated by the nonlinear separation property for cones, a similar separation property for coradiant sets is investigated. A new notion, called Bishop-Phelps coradiant set is introduced and some appropriate properties of this set are studied. This paper also introduces the notions of $$\varepsilon $$ -dual and augmented $$\varepsilon $$ -dual for Bishop and Phelps coradiant sets. Using these notions, some scalarization and characterization properties for $$\varepsilon $$ -efficient and proper $$\varepsilon $$ -efficient points are proposed. [ABSTRACT FROM AUTHOR]

The critical data we share through computer network gets stolen by unethical means. This unethical way of accessing one's data without proper authentication becomes intrusion. To solve this issue, in this paper we propose a new network intrusion detection method, Multi-Class Classification Multiple Criteria Linear Programming (MCC-MCLP) model. MCLP is a mathematical classification technique that is used widely to solve real-time data mining problems. So far, the literature discusses only about binary classification MCLP. But in this paper we propose a Multi-Class Classification MCLP model. We use PSO for fine-tuning the parameters of MCC-MCLP. KDD CUP 99 data set is used for performance evaluation of the proposed method. Our MCC-MCLP method classifies the data better and helps in fine-tuning the parameters with the help of PSO. The results clearly show that the proposed model performs better in terms of detection rate, false alarm rate and accuracy. [ABSTRACT FROM AUTHOR]

We consider in this paper a parallel system consisting of $$\eta $$ identical components. Each component works independently of the others and has a Weibull distributed inter-failure time. When the system fails, we assume that the repair maintenance is imperfect according to the Arithmetic Reduction of Age models ( $$ARA_{m}$$ ) proposed by Doyen and Gaudoin. The purpose of this paper is to generate a simulated failure data of the whole system in order to forecast the behavior of the failure process. Besides, we estimate the maintenance efficiency and the reliability parameters of an imperfect repair following $$ARA_{m}$$ models using maximum likelihood estimation method. Our method is tested with several data sets available from related sources. The real data set corresponds to the time between failures of a compressor which is tested by Likelihood Ratio Test (LR). An analysis of the importance and the effect of the memory order of imperfect repair classes ( $$ARA_{m}$$ ) will be discussed using LR test. [ABSTRACT FROM AUTHOR]

In this paper, we study a vector optimization problem (VOP) with both inequality and equality constraints. We suppose that the functions involved are Fréchet differentiable and their Fréchet derivatives are continuous or stable at the point of study. By virtue of a second-order constraint qualification of Abadie type, we provide second-order Karush-Kuhn-Tucker type necessary optimality conditions for the VOP. Moreover, we also obtain second-order sufficient optimality conditions for a kind of strict local efficiency. Both the necessary conditions and the sufficient conditions are shown in equivalent pairs of primal and dual formulations by using theorems of the alternative for the VOP. [ABSTRACT FROM AUTHOR]

For homothetic time and state separable preferences, the coefficient of relative risk aversion (CRRA) is equal to the reciprocal of the elasticity of intertemporal substitution (EIS). This paper shows that when the growth rate of consumption is i.i.d., asset pricing models based upon preferences in which the CHRA and the EIS are no longer linked do not have more explanatory power. Further, in these stochastic environments, estimates of the CHRA in the standard preferences are measures of the true CHRA and not the EIS. These results are fairly accurate descriptions of economies calibrated using United States annual data. [ABSTRACT FROM AUTHOR]

The Double Row Layout Problem (DRLP) is the problem of allocating a given set of machines on both sides of a straight line corridor so as to minimise the total cost of transporting materials among machines. The DRLP occurs in several manufacturing plants, particularly in semiconductor manufacturing. While it has a large practical importance, the problem is very difficult to solve to optimality. In this paper, we construct a mixed-integer programming (MIP) formulation of the problem, which favourably compares to a previously published MIP formulation. The new model is found to present similar performance to another published MIP formulation, and it has the advantage of being more intuitive for handling qualitative inputs that may be required in a layout refinement phase. [ABSTRACT FROM AUTHOR]

This paper focuses on the design and implementation of green heterogeneous scheduling algorithm based on the theory and technology hotspot of energy saving and emission reduction in cloud computing, since intelligent scheduling algorithms often have defects such as insufficient dynamic optimization power or poor parallel framework design. Following that, a distributed swarm intelligence optimization algorithm for greener heterogeneous scheduling, is proposed, including ⓵ an optimal blending pattern of particle swarm intelligence and nonlinear geometric Brownian motion, based on the related physical sciences and stochastic mathematical analyses, and ⓶ a parallel fusion model that is suitable for the management server processor hybrid system, i.e., coarse-grained parallelism between nodes and CPU/GPU master-slave in a single node. Then, a large number of experimental results are given, whose evaluation indicators can be divided into two categories: static and dynamic optimization performance. Compared with most newly published scheduling algorithms, there are significant advantages of the proposed algorithm on the dynamic optimization performance for consistent or semiconsistent and large inconsistent scheduling instances, although with the lower improvement for the small inconsistent instances. [ABSTRACT FROM AUTHOR]

Most of the works about flowshop scheduling problems assume that the problem data are known exactly in advance or the common approach to the treatment of the uncertainties in the problem is the use of probabilistic models. However, the evaluation and optimization of the probabilistic model is computationally expensive and rational only when the descriptions of the uncertain parameters are available from the historical data. In addition, as in many real-world situations, a certain amount of delay on due dates may be tolerated in most situations although they are handled as crisp dates in most of the previous papers. In this paper we deal with a flowshop scheduling problem with fuzzy processing times and flexible due dates. Schedules are generated by a proposed algorithm in the context of ant colony optimization metaheuristic approach. We use the necessity measure as a confidence measure with which the occurrence of the nontardy schedule can be guaranteed to be certain. [ABSTRACT FROM AUTHOR]

We give an accurate historical and scientific account of a practically unknown manuscript written by Ettore Majorana in French. The retrieved text deals with Quantum Electrodynamics by using the formalism of field quantization, and it is here reported, for the first time, in English translation. It is likely related to an invited talk for a conference at Leningrad (or Kharkov) in 1933 (or 1934) which, however, Majorana never attended. Probably this manuscript is one of the last missing papers of the “Senatore folder”, given by Majorana to one student of his at the University of Naples in 1938, just before his disappearance. [ABSTRACT FROM AUTHOR]

In this paper, we use the penalty approach in order to study constrained minimization problems in infinite dimensional spaces. A penalty function is said to have the exact penalty property if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem. In this paper, we establish the exact penalty property for a large class of inequality-constrained minimization problems. [ABSTRACT FROM AUTHOR]

The focal point of this paper is the probabilistically constrained linear program (PCLP) and how it can be applied to control system, design under risk constraints. The PCLP is the counterpart of the classical linear program, where it is assumed that there is random uncertainty in the constraints and, therefore, the deterministic constraints are replaced by probabilistic ones. It is shown that for a wide class of probability density functions, called log-concave symmetric densities, the PCLP is a convex program. An equivalent formulation of the PCLP is also presented which provides insight into numerical implementation. This concept is applied to control system design. It is shown how the results in this paper can be applied to the design of controllers for discrete-time systems to obtain a closed loop system with a well-defined risk of violating the so-called property of svperstability. Furthermore, we address the problem of risk-adjusted pole placement. [ABSTRACT FROM AUTHOR]

Rufus P. Isaacs joined the RAND Corporation4. Santa Monica, California in 1948 and started to develop the theory of dynamic games in the early 1950s. Until winter 1954/55, when Isaacs left the RAND Corporation, he investigated two player. zero-sum dynamic games of the classic pursuit-evasion type. Prior to 1965, Isaacs published his theory only in internal RAND papers and research memoranda. In his first RAND paper (Ref. 1), Isaacs sketched the basic ideas of zero-sum dynamic game theory The ideas already included rudimentary precursors of the maximum principle, dynamic programming, and backward analysis. At the end of 1954 and the beginning of 1955. Isaacs summarized his research in four research memoranda (Refs. 3–6), which ten years later formed the basis of his famous book on Differential Games (Ref. 7). This paper survey's Isaacs' research with an emphasis on the early years of dynamic games. The readers are kindly invited to discuss the author's point of view. Comments and statements sent to the author will be summarized and published later. [ABSTRACT FROM AUTHOR]

A synergistic perspective to selecting the right project portfolio is the key to realizing strategic organizational objectives. Based on the theory of the composite system, this paper identifies the factors that affect the science of project portfolio selection (PPS) and investigates the synergistic relationship among the organizational strategic objective subsystem, the project portfolio subsystem and the environment subsystem, which collectively constitute the composite system of project portfolio selection. Utilizing the concept of order parameters, an order parameter system is built for each subsystem to reflect the synergistic relationships in the composite system of PPS. The PPS model is constructed based on the degree of synergy in the composite system by describing the order degree of the subsystem and the synergy degree of the composite system, which helps to quantify the synergistic relationships among these subsystems. The effectiveness and feasibility of the proposed model are demonstrated and validated by a case study. [ABSTRACT FROM AUTHOR]