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Much is known about when a locally optimal solution depends in a single-valued Lipschitz continuous way on the problem's parameters, including tilt perturbations. Much less is known, however, about when that solution and a uniquely determined multiplier vector associated with it exhibit that dependence as a primal–dual pair. In classical nonlinear programming, such advantageous behavior is tied to the combination of the standard strong second-order sufficient condition (SSOC) for local optimality and the linear independent gradient condition (LIGC) on the active constraint gradients. But although second-order sufficient conditons have successfully been extended far beyond nonlinear programming, insights into what should replace constraint gradient independence as the extended dual counterpart have been lacking. The exact answer is provided here for a wide range of optimization problems in finite dimensions. Behind it are advances in how coderivatives and strict graphical derivatives can be deployed. New results about strong metric regularity in solving variational inequalities and generalized equations are obtained from that as well. [ABSTRACT FROM AUTHOR]

For the problem of trajectory planning in the small-scale unmanned aerial vehicle (UAV) swarms, classical intelligent algorithms and newly emerged bio-inspired algorithms often suffer from being trapped in local optima, leading to suboptimal solutions. Moreover, these algorithms fail to ensure optimal solutions and convergence speed in high-speed dynamic UAV networking scenarios. In response to these challenges, this paper proposes an Improved Whale Optimization Algorithm (IWOA) that considers the global perspective. To address the issue of initial solution diversity, an opposition-based learning method is introduced by constructing a reverse population, enhancing the diversity of the initial population. To overcome the problem of the algorithm getting trapped in local optima, random convergence factors, and end-point random neighborhood perturbations are incorporated to accelerate the global convergence speed of the IWOA and prevent it from getting stuck in local optima. Additionally, a grid digital elevation model is employed when constructing the experimental environment model, considering various physical constraints of the UAV swarm. This ensures that the simulation validation of the IWOA algorithm is closer to real-world scenarios. Simulation results indicate that, compared to commonly used algorithms, the IWOA can generate more optimal trajectories for drone swarm planning under constraints resembling real-world scenarios. It exhibits better performance in trajectory evaluation, convergence speed, and stability, thereby meeting the requirements of trajectory planning for small-scale UAV swarms. The proposed IWOA enhances UAV swarm coordination and efficiency, significantly impacting real-world applications in various fields. [ABSTRACT FROM AUTHOR]

The economic dispatch (ED) problem is very important in the economics of power systems, and a suitable dispatch algorithm can help power plants save huge amounts of money and use energy efficiently. To ensure the economics of the power system dispatch strategy, this paper proposes a quantum‐behaved particle swarm improvement algorithm for solving the ED problem. First, the algorithm addresses the problem that the classical quantum‐behaved particle swarm optimization (QPSO) tends to be premature and falls into local optimality. We propose a method to calculate the mean best position by assigning weights to different particles, by adopting the idea of concentration selection in the immune concentration regulation mechanism, and designing a Weight‐Concentration selection probability function, so that those particles located outside the local optimal solution region but with smaller fitness value and better evolutionary trend can be retained. Second, to make the algorithm focus on global search at the beginning of the iteration and more focused search at the end to enhance the neighborhood search capability at the later stage, a decreasing function of the slope K in the Weight‐Concentration selection probability function is designed so that the influence of the weighting term on the calculation of the mean best position decreases gradually. The algorithm is evaluated with four power systems, and the results show that the overall performance of the improved algorithm is better than other algorithms in solving the ED problem in terms of minimum solution, convergence, and stability. © 2024 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

Among steganalysis techniques, detection against MV (motion vector) domain-based video steganography in the HEVC (High Efficiency Video Coding) standard remains a challenging issue. For the purpose of improving the detection performance, this paper proposes a steganalysis method that can perfectly detect MV-based steganography in HEVC. Firstly, we define the local optimality of MVP (Motion Vector Prediction) based on the technology of AMVP (Advanced Motion Vector Prediction). Secondly, we analyze that in HEVC video, message embedding either using MVP index or MVD (Motion Vector Difference) may destroy the above optimality of MVP. And then, we define the optimal rate of MVP as a steganalysis feature. Finally, we conduct steganalysis detection experiments on two general datasets for three popular steganography methods and compare the performance with four state-of-the-art steganalysis methods. The experimental results demonstrate the effectiveness of the proposed feature set. Furthermore, our method stands out for its practical applicability, requiring no model training and exhibiting low computational complexity, making it a viable solution for real-world scenarios. [ABSTRACT FROM AUTHOR]

Orthogonally decomposable (odeco) tensors is a special class of symmetric tensors. Previous works have focused on investigating its E-eigenpairs problem, and made some theoretical achievements concerning the number and the local optimality of E-eigenpairs. However, concerning local optimality of each eigenpair, the existing work only analyzed the third-order tensor case. In this paper, we further exploit this issue for any higher-order tensors by checking second-order necessary condition of the related constrained optimization model and deducing an equivalent matrix formula criterion for local optimality identification. Finally, a generalized conclusion for local optimality of eigenpairs for odeco tensors is provided, and some simulated experiments are conducted for validation. [ABSTRACT FROM AUTHOR]

With the rapid development of science and technology and the impact of the novel coronavirus epidemic in recent years, medical delivery robots have gradually appeared in major medical institutions. However, traditional medical delivery robots have local optimal solution problems and target unreachable problems when using artificial potential field algorithms for path planning. Therefore, for the local optimal solution problem, this paper proposes a method of designing virtual target points to rescue the robot from the local optimal state. In this paper, the target distance function is introduced into obstacle repulsion potential field function to limit obstacle repulsion, to solve the problem of target unreachable. Finally, the proposed method is compared with the traditional algorithm in a variety of complex environments. The results show that the improved algorithm can solve the local optimal solution and target unreachable problems existing in the traditional algorithm, and the efficiency of the algorithm is also increased by 5%-9% and can be effectively applied to practical scenarios. [ABSTRACT FROM AUTHOR]

Quadratic unconstrained binary optimization (QUBO) is a classic NP-hard problem with an enormous number of applications. Local search strategy (LSS) is one of the most fundamental algorithmic concepts and has been successfully applied to a wide range of hard combinatorial optimization problems. One LSS that has gained the attention of researchers is the r-flip (also known as r-Opt) strategy. Given a binary solution with n variables, the r-flip strategy "flips" r binary variables to obtain a new solution if the changes improve the objective function. The main purpose of this paper is to develop several results for the implementation of r-flip moves in QUBO, including a necessary and sufficient condition that when a 1-flip search reaches local optimality, the number of candidates for implementation of the r-flip moves can be reduced significantly. The results of the substantial computational experiments are reported to compare an r-flip strategy-embedded algorithm and a multiple start tabu search algorithm on a set of benchmark instances and three very-large-scale QUBO instances. The r-flip strategy implemented within the algorithm makes the algorithm very efficient, leading to very high-quality solutions within a short CPU time. [ABSTRACT FROM AUTHOR]

This paper focuses on the local optimality for the stationary points of the composite group zero-norm regularized problem and its equivalent surrogates. First, by using the structure of the composite group zero-norm and its second subderivative characterization, we achieve several local optimal conditions for a stationary point of the group zero-norm regularized problem. Then, we obtain a family of equivalent surrogates for the group zero-norm regularized problem from a class of global exact penalties of its MPEC reformulation, established under the calmness of a partial perturbation to the composite group zero-norm constraint system. For the stationary points of these surrogates, we study their local optimality to the surrogates themselves and the group zero-norm regularized problem. The local optimality conditions obtained in this work not only recover the existing ones for zero-norm regularized problems, but also provide new criteria to judge the local optimality of a stationary point yielded by an algorithm for solving the corresponding surrogate problems. [ABSTRACT FROM AUTHOR]

In response to the limitations observed in the Intelligent Water Droplet (IWD) algorithm for path planning, including its weak problem-solving capability and susceptibility to local optimization, this paper presents an enhanced Intelligent Water Droplet algorithm. The improved algorithm incorporates the distance factor between nodes and the target point into the original algorithm’s path probability, enhancing its problem-solving prowess and expediting algorithmic convergence. Simultaneously, a roulette-based probability selection method is introduced to circumvent local optimization during the solution process. Additionally, the algorithm is coupled with the Floyd algorithm to refine the planned path, reducing the number of inflection points to align with the motion characteristics of the inspection robot. Simulation results underscore the effectiveness of the enhanced Intelligent Water Droplet algorithm in mitigating the impact of local optimization in path planning. In comparison to the original IWD algorithm, the optimized path exhibits a 17.42% reduction in length, a 58.3% decrease in the minimum number of iterations required for path convergence, and a 36.3% reduction in the number of path inflection points. Furthermore, the total path length is decreased by 7.7% following path optimization via the Floyd algorithm.

Quadratic unconstrained binary optimization (QUBO) is a classic NP-hard problem with an enormous number of applications. Local search strategy (LSS) is one of the most fundamental algorithmic concepts and has been successfully applied to a wide range of hard combinatorial optimization problems. One LSS that has gained the attention of researchers is the r-flip (also known as r-Opt) strategy. Given a binary solution with n variables, the r-flip strategy “flips” r binary variables to obtain a new solution if the changes improve the objective function. The main purpose of this paper is to develop several results for the implementation of r-flip moves in QUBO, including a necessary and sufficient condition that when a 1-flip search reaches local optimality, the number of candidates for implementation of the r-flip moves can be reduced significantly. The results of the substantial computational experiments are reported to compare an r-flip strategy-embedded algorithm and a multiple start tabu search algorithm on a set of benchmark instances and three very-large-scale QUBO instances. The r-flip strategy implemented within the algorithm makes the algorithm very efficient, leading to very high-quality solutions within a short CPU time.

In this letter, a novel steganographic scheme in motion vector domain (MV) for H.264 video is presented, which can significantly improve the security performance against the newly emerged powerful multi-domain feature set MVC (motion vector consistency). By taking into account both the consistency degree of motion vectors for sub-blocks within a macroblock (MB) or sub-macroblock (sub-MB), and the MV statistics, the corresponding distortion function called dMVC is proposed. The proposed dMVC is also shown to be capable of integrating with existing methods to resist the joint steganalytic attacks of both MVC feature and local optimality features, e.g., NPELO, in the framework of minimal distortion embedding. Compared with other state-of-the-art MV-based steganographic schemes, experimental results on YUV sequences at various embedding rates and QPs show that the proposed method gains significant performance improvement while maintaining good coding efficiency. [ABSTRACT FROM AUTHOR]

Convergence to a saddle point for convex-concave functions has been studied for decades, while recent years has seen a surge of interest in non-convex (zero-sum) smooth games, motivated by their recent wide applications. It remains an intriguing research challenge how local optimal points are defined and which algorithm can converge to such points. An interesting concept is known as the local minimax point (Jin et al., 2020), which strongly correlates with the widely-known gradient descent ascent algorithm. This paper aims to provide a comprehensive analysis of local minimax points, such as their relation with other solution concepts and their optimality conditions. We find that local saddle points can be regarded as a special type of local minimax points, called uniformly local minimax points, under mild continuity assumptions. In (non-convex) quadratic games, we show that local minimax points are (in some sense) equivalent to global minimax points. Finally, we study the stability of gradient algorithms near local minimax points. Although gradient algorithms can converge to local/global minimax points in the non-degenerate case, they would often fail in general cases. This implies the necessity of either novel algorithms or concepts beyond saddle points and minimax points in non-convex smooth games. [ABSTRACT FROM AUTHOR]

• Previous steganalytic methods cannot detect HEVC-exclusive MV modification strategy that keeps the MV values unchanged. • We find out the local optimality in candidate list can better characterize the perturbation for MV modification. • We proposed a new HEVC steganalytic method based on a 40-dimensional feature set. • Our method outperforms existing ones against both the traditional and the HEVC-exclusive MV modifications. Current research of video steganalysis is mainly oriented to H.264 or even earlier formats. As the H.265/HEVC standard is becoming more and more popular, there have been steganographic methods specifically designed for HEVC videos. Previous steganalytic methods are no longer effective due to the new features of HEVC. The advanced motion vector prediction technique employed by HEVC provides a new way for motion vector (MV) modification, utilizing the index of the candidate MV list. Such modification cannot be detected by previous steganalytic methods because the value of MV is not changed. To solve this problem, we proposed a new steganalytic strategy employing not only the local optimality of MV but also the local optimality in the candidate list. Combining the two types of local optimality, a 40-dimensional feature set is designed. Extensive experiments are carried out to evaluate the effectiveness of the proposed feature set. It is shown that compared with three current steganalyzers, our approach improves the performance against typical MV modification methods under various settings. In particular, our approach significantly boosts the detection accuracy of the index modification method that is exclusive to HEVC videos. To our best knowledge, this is the first work of video steganalytic method exploiting the new features of HEVC format. [ABSTRACT FROM AUTHOR]

The generalized Pareto model plays an important role in modelling extreme events. Hosking and Wallis (1987) discussed the parameter and quantile estimation for generalized Pareto distribution. Optimal experimental designs are used to accurately estimate the unknown parameters of the model. In this paper, locally D-, A- and E-optimal designs with two and three support points having equal and unequal weights for homoscedastic generalized Pareto regression model are obtained numerically. It is also proved that these designs are minimally supported. The results are illustrated through Norwegian fire insurance claim data.

In this work, the local optimality of mixed reliability of networks is surveyed. A reliability comparison criterion related with subgraphs to measure the local optimality of the mixed reliability of networks is established. Using the comparison criterion, we characterize all locally optimally mixed reliable networks among all n-vertex networks with fixed sizes m=n, m=n+1 and m=n+2, respectively.

• Local optimality is suggested as a criterion to characterize route choice candidates. • Locally optimal routes have a mechanistic justification and require minimal data. • An algorithm to find locally optimal routes is presented and tested. • The approach is efficient in large systems, facilitates comprehensive traffic models. • Locally optimal routes yield good predictions of where travellers can be observed. Route choice is often modelled as a two-step procedure in which travellers choose their routes from small sets of promising candidates. Many methods developed to identify such choice sets rely on assumptions about the mechanisms behind the route choice and require corresponding data sets. Furthermore, existing approaches often involve considerable complexity or perform many repeated shortest path queries. This makes it difficult to apply these methods in comprehensive models with numerous origin-destination pairs. In this paper, we address these issues by developing an algorithm that efficiently identifies locally optimal routes. Such paths arise from travellers acting rationally on local scales, whereas unknown factors may affect the routes on larger scales. Though methods identifying locally optimal routes are available already, these algorithms rely on approximations and return only few, heuristically chosen paths for specific origin-destination pairs. This conflicts with the demands of route choice models, where an exhaustive search for many origins and destinations would be necessary. We therefore extend existing algorithms to return (almost) all admissible paths between a large number of origin-destination pairs. We test our algorithm and its applicability in route choice models on the road network of the Canadian province British Columbia and empirical data collected in this province. [ABSTRACT FROM AUTHOR]

This paper presents a procedure which composes music pieces through handling four layers in music, namely pitches, rhythms, dynamics, and timber. As an innovative feature, the procedure uses the combination of a genetic algorithm with a synergetic variable neighbourhood search. Uniform and one-point crossover operators as well as two mutation operators conduct the search in the employed genetic algorithm. The key point with these four operators is that the uniform crossover operator and the first mutation operator are indiscriminate, in the sense of using no knowledge of music theory, whereas the employed one-point crossover operator and the second mutation operator are musically informed. Music theory is used for finding the suitability of its generated pieces. The method starts with generating an initial sequence of pitches with a musically informed module and then calculates the suitability of the pitch sequence through the embedded rules. The employed genetic algorithm applies the variable neighbourhood search method to its generated offspring genomes for increasing their quality. Pieces can be composed in major, minor, and harmonic minor scales based on the user's request. As well as composing the main notes, the procedure generates up to three chord notes associated with each main note and plays the result in a novel multithreading environment through running four threads concurrently. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a detailed mathematical analysis of the optimality of the premise and consequent parts of the recently introduced first-order Autonomous Learning Multi-Model (ALMMo) neuro-fuzzy system is conducted. A novel self-boosting algorithm for structure- and parameter-optimization is, then, introduced to the ALMMo, which results in the self-boosting ALMMo (SBALMMo) neuro-fuzzy system. By minimizing the objective functions with the previously collected data, the SBALMMo is able to optimize its system structure and parameters in few iterations. Numerical examples based benchmark datasets and real-world problems demonstrate the effectiveness and validity of the SBALMMo, and show the strong potential of the proposed approach for real applications. Highlights • A systematic analysis of the optimality of the ALMMo neuro-fuzzy system is conducted. • A novel self-boosting algorithm for structure and parameter-optimization is proposed. • The self-boosting ALMMo (SBALMMo) neuro-fuzzy system is introduced. • The effectiveness and validity of the SBALMMo are demonstrated on real world problems. [ABSTRACT FROM AUTHOR]

It is well-known that normal extremals in sub-Riemannian geometry are curves that locally minimize the length functional (equivalently, the energy functional). Most proofs of this fact do not make, however, an explicit use of relations between local optimality and the geometry of the problem. In this paper, we provide a new proof of that classical result, which gives insight into direct geometric reasons for local optimality. Also the relation of the regularity of normal extremals with their optimality becomes apparent in our approach. [ABSTRACT FROM AUTHOR]

Cost assignment in the motion vector domain remains a research focus in video steganography. Recent studies in image steganography have summarized many principles for cost assignment and achieved good results. But the basic principles for cost assignment in motion vector-based video steganography have not been fully discussed yet. Firstly, this paper proposes three principles for cost assignment in the motion vector domain, including the principle of local optimality, non-consistency in the block group, and complexity priority. Secondly, three corresponding novel practical distortion functions were designed according to the three principles. Finally, a joint distortion function is constructed based on all three principles to increase overall performance. The experimental results show that not only the three independent distortion functions can effectively resist the corresponding steganalysis attacks, but the final joint distortion can resist the three steganalysis features simultaneously. In addition, it can obtain good visual quality and coding efficiency, which can be applied to practical scenarios. [ABSTRACT FROM AUTHOR]

Current motion vector based video steganography is unable to preserve the local optimality of modified motion vectors. Thus they are vulnerable to the attack of steganalysis. In this paper, we have proposed a novel method to guarantee the local optimality of modified motion vectors. To modify a motion vector, firstly designate a search area which consists of candidate motion vectors. Second, evaluate the local optimality of each motion vector in the search area to locate all local optimum ones, from which finally select the one contributing least to video compression efficiency degradation as the modified motion vector. Highly undetectable motion vector based video steganography can be developed by combining the proposed method with steganographic codes and reasonable cost assignment. Comparative experimental results have demonstrated that video steganography based on the proposed method is capable of withstanding current best steganalysis while keeping the video compression performance. [ABSTRACT FROM AUTHOR]

This paper studies several classes of nonconvex optimization problems defined over convex cones, establishing connections between them and demonstrating that they can be equivalently formulated as convex completely positive programs. The problems being studied include: a conic quadratically constrained quadratic program (QCQP), a conic quadratic program with complementarity constraints (QPCC), and rank constrained semidefinite programs. Our results do not make any boundedness assumptions on the feasible regions of the various problems considered. The first stage in the reformulation is to cast the problem as a conic QCQP with just one nonconvex constraint $$q(x) \le 0$$ , where q( x) is nonnegative over the (convex) conic and linear constraints, so the problem fails the Slater constraint qualification. A conic QPCC has such a structure; we prove the converse, namely that any conic QCQP satisfying a constraint qualification can be expressed as an equivalent conic QPCC. The second stage of the reformulation lifts the problem to a completely positive program, and exploits and generalizes a result of Burer. We also show that a Frank-Wolfe type result holds for a subclass of this class of conic QCQPs. Further, we derive necessary and sufficient optimality conditions for nonlinear programs where the only nonconvex constraint is a quadratic constraint of the structure considered elsewhere in the paper. [ABSTRACT FROM AUTHOR]

Discrete choice experiments are widely used in fields such as marketing, planning, transportation, and medical care to obtain information on consumer preferences. In such experiments, choice sets consisting of two or more profiles are presented to subjects, where a profile consists of a set of attributes (as a list or picture) which describe the product or process. Subjects are asked to select their most preferred profile from each choice set, and the importance of the attributes can be deduced from the choices made. This paper investigates locally A-optimal designs for estimating main effects of the attributes, together with their interactions, under the multinomial logit model. Lower bounds are derived for the average variance of any set of orthonormal contrasts of interest. A new approach is proposed for generating locally A-optimal or A-efficient designs. It is shown through examples that the new construction method enables highly efficient designs to be constructed without a complete search. [ABSTRACT FROM AUTHOR]

We consider decoding of binary linear Tanner codes using message-passing iterative decoding and linear-programming (LP) decoding in memoryless binary-input output-symmetric (MBIOS) channels. We present new certificates that are based on a combinatorial characterization for the local optimality of a codeword in irregular Tanner codes with respect to any MBIOS channel. This characterization is a generalization of (Arora , Proc. ACM Symp. Theory of Computing, 2009) and (Vontobel, Proc. Inf. Theory and Appl. Workshop, 2010) and is based on a conical combination of normalized weighted subtrees in the computation trees of the Tanner graph. These subtrees may have any finite height h (even equal or greater than half of the girth of the Tanner graph). In addition, the degrees of local-code nodes in these subtrees are not restricted to two (i.e., these subtrees are not restricted to skinny trees). We prove that local optimality in this new characterization implies maximum-likelihood (ML) optimality and LP optimality, and show that a certificate can be computed efficiently. We also present a new message-passing iterative decoding algorithm, called normalized weighted min-sum (NWMS). NWMS decoding is a belief-propagation (BP) type algorithm that applies to any irregular binary Tanner code with single parity-check local codes (e.g., low-density and high-density parity-check codes). We prove that if a locally optimal codeword with respect to height parameter h exists (whereby notably h is not limited by the girth of the Tanner graph), then NWMS decoding finds this codeword in h iterations. The decoding guarantee of the NWMS decoding algorithm applies whenever there exists a locally optimal codeword. Because local optimality of a codeword implies that it is the unique ML codeword, the decoding guarantee also provides an ML certificate for this codeword. Finally, we apply the new local-optimality characterization to regular Tanner codes, and prove lower bounds on the noise thresholds of LP decoding in MBIOS channels. When the noise is below these lower bounds, the probability that LP decoding fails to decode the transmitted codeword decays doubly exponentially in the girth of the Tanner graph. [ABSTRACT FROM PUBLISHER]

This paper presents a unified analysis framework that captures recent advances in the study of local-optimality characterizations for codes on graphs. These local-optimality characterizations are based on combinatorial structures embedded in the Tanner graph of the code. Local optimality implies both unique maximum likelihood optimality and unique linear programming (LP) decoding optimality. Also, an iterative message-passing decoding algorithm is guaranteed to find the unique locally optimal codeword if one exists. We demonstrate an instance of this proof technique by considering a definition of local optimality that is based on the simplest combinatorial structures in Tanner graphs, namely, paths of length h. We apply the technique of local optimality to binary Tanner codes (including any low-density parity-check code, and in particular any irregular repeat-accumulate code with both even and odd repetition factors). Inverse polynomial bounds in the code length are proved on the word error probability of LP decoding for binary Tanner codes. When the local codes are restricted to single parity-check codes, these bounds also hold for decoding by a certain iterative message-passing decoding algorithm. [ABSTRACT FROM AUTHOR]

The question of whether phonologically-conditioned suppletive allomorphy can ever be outwardly sensitive has been a key point of contention in debates between parallel and serial theories of morpho-phonology. Purely serial theories bar outwardssensitivity altogether, while parallel theories permit it across the board. A few examples have been reported, demonstrating the need for some degree of parallelism, but are sufficiently limited to suggest that some degree of serialism is also required. This paper advances a proposal regarding when allomorphs compete serially and when they compete in parallel. Specifically, it proposes that there is a connection between outwards-sensitivity and feature mismatches in morphological spell-out, and suggests a revision to the theory of Optimal Interleaving (OI: Wolf in Optimal interleaving: serial phonology-morphology interaction in a constraint-based model, 2008 ) which captures this connection. A proposal is also made regarding how to model outwards-sensitive root allomorphy under OI’s assumptions. [ABSTRACT FROM AUTHOR]

Gompertz functions have been widely used in characterizing biological growth curves. In this paper we consider D-optimal designs for Gompertz regression models. For homoscedastic Gompertz regression models with two or three parameters, we prove that D-optimal designs are minimally supported. Considering that minimally supported designs might not be applicable in practice, alternative designs are proposed. Using the D-optimal designs as benchmark designs, these alternative designs are found to be efficient in general. [ABSTRACT FROM AUTHOR]

Model predictive control (MPC) is one of the few techniques which is able to handle constraints on both state and input of the plant. The admissible evolution and asymptotic convergence of the closed-loop system is ensured by means of suitable choice of the terminal cost and terminal constraint. However, most of the existing results on MPC are designed for a regulation problem. If the desired steady-state changes, the MPC controller must be redesigned to guarantee the feasibility of the optimisation problem, the admissible evolution as well as the asymptotic stability. Recently, a novel MPC has been proposed to ensure the feasibility of the optimisation problem, constraints satisfaction and asymptotic evolution of the system to any admissible target steady-state. A drawback of this controller is the loss of a desirable property of the MPC controllers: the local optimality property. In this article, a novel formulation of the MPC for tracking is proposed aimed to recover the optimality property maintaining all the properties of the original formulation. [ABSTRACT FROM AUTHOR]

Abstract: Most growth curves can only be used to model the tumor growth under no intervention. To model the growth curves for treated tumor, both the growth delay due to the treatment and the regrowth of the tumor after the treatment need to be taken into account. In this paper, we consider two tumor regrowth models and determine the locally D- and c-optimal designs for these models. We then show that the locally D- and c-optimal designs are minimally supported. We also consider two equally spaced designs as alternative designs and evaluate their efficiencies. [ABSTRACT FROM AUTHOR]

Abstract: Logistic functions are used in different applications, including biological growth studies and assay data analysis. Locally D-optimal designs for logistic models with three and four parameters are investigated. It is shown that these designs are minimally supported. Efficiencies are computed for equally spaced and uniform designs. [Copyright &y& Elsevier]

We deal with the differential conditions for local optimality. The conditions that we derive for inequality constrained problems do not require constraint qualifications and are the broadest conditions based on only first-order and second-order derivatives. A similar result is proved for equality constrained problems, although the necessary conditions require the regularity of the equality constraints. [ABSTRACT FROM AUTHOR]

The concept of M-convex functions is generalized for functions defined on constant-parity jump systems. M-convex functions arise from minimum weight perfect b-matchings and from a separable convex function (sum of univariate convex functions) on the degree sequences of an undirected graph. As a generalization of a recent result of Apollonio and Sebő for the minsquare factor problem, a local optimality criterion is given for minimization of an M-convex function subject to a component sum constraint. [ABSTRACT FROM AUTHOR]

The problem of finding a local or a global minimum of a real function on a set S⊆ n occurs in many real world problems. When f is a general nonlinear function, deterministic as well as stochastic algorithms have been proposed. The numerical cost of these algorithms, that can be the number of function evaluations or the number of elementary operations required when executed, has been investigated in the last few years. In this paper, we survey the main results by classifying them according to the field they refer to: local minimization, global minimization and checking the optimality conditions. Further, some results concerning the information that an algorithm may use, are surveyed. [ABSTRACT FROM AUTHOR]

Multimodular functions and L-convex functions have been investigated almost independently, but they are, in fact, equivalent objects that can be related through a unimodular coordinate transformation. Some facts known for L-convex functions can be translated to new results for multimodular functions, and vice versa. In particular, the local optimality condition for global optimality found in the literature of multimodular functions should be rectified, and a discrete separation theorem holds for multimodular functions. [ABSTRACT FROM AUTHOR]

Adaptive optimality of local populations is central to evolutionary biology. It also provides a genetic framework for planning gene conservation. We examined local optimality using 20-year height growth as an indicator of population fitness. The height growth data were obtained from a network of 57 long-term field trials in interior British Columbia involving a range-wide samples of 142 lodgepole pine (Pinus contorta Doug) populations. Local optimality was defined statistically and tested, and its geographic patterns were examined in both multi-dimensional mode and component dimensions along latitude, longitude and elevation. Fitness values of local and optimal populations were derived by fitting population variation to response functions for individual sites. Local optimality was an interval estimate, i.e. within the 95% confidence limit of the projected fitness value of the optimal populations. Both biological and physical distances between local and optimal population were used to examine geographic pattern of local optimality.Study leads to following key results: (1) local optimality prevails at majority of sites; (2) populations at northeast bordering the northern Rocky Mountain Trench are most local optimal, whereas non-local optimality most evident along the eastern foothills of the Coastal Mountains in the coast-interior transition climate zone and the high mountains in the southern interior; (3) there is a geographic cline oriented from southwest to northeast, but with a steep west-east incline; and (4) along component dimensions, a steep longitudinal cline, i.e. the farther the west, the lesser the local optimality, and an elevational cline, i.e. the higher the elevation, the lesser the local optimality.Based on the ecological and life-history characteristics of the species and the climate in interior British Columbia, we propose that a selection gradient coupled with directional gene flow was the process influencing the formation of the observed geographic pattern. The selection gradient parallels the general climate pattern from continental northeast to sub-continental southwest. The gene flow brought the migration of undesirable genes from the coastal subspecies contorta to interior populations of the subspecies latifolia, which further diminished the effectiveness of natural selection. Practical applications through seed transfer in reforestation and genetic resources management are discussed. [Copyright &y& Elsevier]

Viral dynamic and pharmacokinetic models often involve an exponential decay. In this paper, locally D- and c-optimal designs are derived analytically for exponential decay models with one to three parameters. Invariance of optimal designs to reparametrization is discussed and examples of Bayesian optimal designs are also provided. [Copyright &y& Elsevier]

The problem of finding a regular n-dimensional crosspolytope (or simplex) of maximal volume in an n-dimensional cube subsumes the famous problem about the existence of Hadamard matrices. In this paper it is shown that the crosspolytope problem also has a connection to another important class of matrices, the symmetric conference matrices. It is shown that symmetric conference matrices are closely related to crosspolytopes that are locally optimal, in a certain natural sense. Some open questions about the local optimality of crosspolytopes related to other matrices (in particular, to weighing matrices) are also presented. [Copyright &y& Elsevier]