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In this short paper, we look into a conclusion drawn by Alzalg (J Optim Theory Appl 169:32-49, 2016). We think the conclusion drawn in the paper is incorrect by pointing out three things. First, we provide a counterexample that the proposed inner product does not satisfy bilinearity. Secondly, we offer an argument why a pth-order cone cannot be self-dual under any reasonable inner product structure on $$\mathbb {R}^n$$ . Thirdly, even under the assumption that all elements operator commute, the inner product becomes an official inner product and the arbitrary-order cone can be shown as a symmetric cone, we think this condition is still unreasonable and very stringent so that the result can only be applied to very few cases. [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]

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."

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

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.

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]

In this paper, we study the link between a Chance-Constrained optimization Problem (CCP) and its sample counterpart (SP). SP has a finite number, say N, of sampled constraints. Further, some of these sampled constraints, say k, are discarded, and the final solution is indicated by $x^{\ast}_{N,k}$. Extending previous results on the feasibility of sample convex optimization programs, we establish the feasibility of $x^{\ast}_{N,k}$ for the initial CCP problem. Constraints removal allows one to improve the cost function at the price of a decreased feasibility. The cost improvement can be inspected directly from the optimization result, while the theory here developed permits to keep control on the other side of the coin, the feasibility of the obtained solution. In this way, trading feasibility for performance is put on solid mathematical grounds in this paper. The feasibility result here obtained applies to a vast class of chance-constrained optimization problems, and has the distinctive feature that it holds true irrespective of the algorithm used to discard k constraints in the SP problem. For constraints discarding, one can thus, e.g., resort to one of the many methods introduced in the literature to solve chance-constrained problems with discrete distribution, or even use a greedy algorithm, which is computationally very low-demanding, and the feasibility result remains intact. We further prove that, if constraints in the SP problem are optimally removed-i.e., one deletes those constraints leading to the largest possible cost improvement-, then a precise optimality link to the original chance-constrained problem CCP in addition holds. [ABSTRACT FROM AUTHOR]

An interior-point method (IPM) defines a search direction at each interior point of the feasible region. These search directions form a direction field, which in turn gives rise to a system of ordinary differential equations (ODEs). Thus, it is natural to define the underlying paths of the IPM as the solutions of the system of ODEs. In Sim and Zhao (Math. Program. Ser. A, 2007, to appear), these off-central paths are shown to be well-defined analytic curves and any of their accumulation points is a solution to the given monotone semidefinite linear complementarity problem (SDLCP). Off-central paths for a simple example are also studied in Sim and Zhao (Math. Program. Ser. A, 2007, to appear) and their asymptotic behavior near the solution of the example is analyzed. In this paper, which is an extension of Sim and Zhao (Math. Program. Ser. A, 2007, to appear), we study the asymptotic behavior of the off-central paths for general SDLCPs using the dual HKM direction. We give a necessary and sufficient condition for when an off-central path is analytic as a function of vμ at a solution of the SDLCP. Then, we show that, if the given SDLCP has a unique solution, the first derivative of its off-central path, as a function of vμ, is bounded. We work under the assumption that the given SDLCP satisfies the strict complementarity condition. An interior-point method (IPM) defines a search direction at each interior point of the feasible region. These search directions form a direction field, which in turn gives rise to a system of ordinary differential equations (ODEs). Thus, it is natural to define the underlying paths of the IPM as the solutions of the system of ODEs. In Sim and Zhao (Math. Program. Ser. A, 2007, to appear), these off-central paths are shown to be well-defined analytic curves and any of their accumulation points is a solution to the given monotone semidefinite linear complementarity problem (SDLCP). Off-central paths for a simple example are also studied in Sim and Zhao (Math. Program. Ser. A, 2007, to appear) and their asymptotic behavior near the solution of the example is analyzed. In this paper, which is an extension of Sim and Zhao (Math. Program. Ser. A, 2007, to appear), we study the asymptotic behavior of the off-central paths for general SDLCPs using the dual HKM direction. We give a necessary and sufficient condition for when an off-central path is analytic as a function of √μ at a solution of the SDLCP. Then, we show that, if the given SDLCP has a unique solution, the first derivative of its off-central path, as a function of √μ, is bounded. We work under the assumption that the given SDLCP satisfies the strict complementarity condition. [ABSTRACT FROM AUTHOR]

This paper studies the tracking and almost disturbance decoupling problem of the nonlinear AMIRA ball and beam system based on the feedback linearization approach. The main contribution of this study is to construct a controller, under appropriate conditions, such that the resulting closed-loop system is valid for any initial condition and bounded tracking signal with the following characteristics: input-to-state stability with respect to disturbance inputs and almost disturbance decoupling. Two examples on the almost disturbance decoupling problem, which cannot be solved via Ref. 1, are proposed in this paper exploiting the fact that the tracking and the almost disturbance decoupling performances are easily achieved by our proposed approach. [ABSTRACT FROM AUTHOR]

A composite control law for stabilizing a small-scale helicopter during hover flight mode is proposed in this paper. The proposed method is developed by combining the sliding mode control (SMC) and a nonlinear control law. Parameters of the proposed controller are optimized using particle swarm optimization technique. The SMC ensures robustness under disturbances and parameter uncertainties, while the nonlinear control law improves the transient response of the closed-loop system. Adequacy of the combination of the sliding mode controller and the nonlinear control law is validated using mathematical analysis and simulation experiments. The results illustrate an efficient execution of the proposed controller to stabilize the system by reducing the deviations from the trim state and alleviating the effect of disturbance in the closed-loop response. [ABSTRACT FROM AUTHOR]

In this paper, a new sequential penalty algorithm, based on the L[sub ∞] exact penalty function, is proposed for a general nonlinear constrained optimization problem. The algorithm has the following characteristics: it can start from an arbitrary initial point; the feasibility of the subproblem is guaranteed; the penalty parameter is adjusted automatically; global convergence without any regularity assumption is proved. The update formula of the penalty parameter is new. It is proved that the algorithm proposed in this paper behaves equivalently to the standard SQP method after sufficiently many iterations. Hence, the local convergence results of the standard SQP method can be applied to this algorithm. Preliminary numerical experiments show the efficiency and stability of the algorithm. [ABSTRACT FROM AUTHOR]

In multiple-objective optimization literature, a properly efficient solution has been interpreted as a point in which the trade-offs between all objectives are bounded. In this paper, it is shown that this boundedness does not necessarily hold for problems with three or more objective functions. It is possible that in a properly efficient solution the trade-offs between some objectives are unbounded. To overcome this, in this paper strongly proper efficient solutions are introduced, in which the trade-offs between all objectives are bounded. This notion is defined in different senses, and the relationships between them are investigated. In addition to theoretical discussions, some clarifying examples are given. [ABSTRACT FROM AUTHOR]

This paper presents new approximation bounds for trilinear and biquadratic optimization problems over nonconvex constraints. We first consider the partial semidefinite relaxation of the original problem, and show that there is a bounded approximation solution to it. This will be achieved by determining the diameters of certain convex bodies. We then show that there is also a bounded approximation solution to the original problem via extracting the approximation solution of its semidefinite relaxation. Under some conditions, the approximation bounds obtained in this paper improve those in the literature. [ABSTRACT FROM AUTHOR]

We study the uniqueness and explicit derivation of the relaxed optimal solutions, corresponding to the minimization of weighted sum of potential energies for a mixture of two isotropic conductive materials on an annulus. Recently, it has been shown by Burazin and Vrdoljak that even for multiple-state problems, if the domain is spherically symmetric, then the proper relaxation of the problem by the homogenization method is equivalent to a simpler relaxed problem, stated only in terms of local proportions of given materials. This enabled explicit calculation of a solution on a ball, while problems on an annulus appeared to be more tedious. In this paper, we discuss the uniqueness of a solution of this simpler relaxed problem, when the domain is an annulus and we use the necessary and sufficient conditions of optimality to present a method for explicit calculation of the unique solution of this simpler proper relaxation, which is demonstrated on an example. [ABSTRACT FROM AUTHOR]

Multiobjective optimization has a significant number of real-life applications. For this reason, in this paper we consider the problem of finding Pareto critical points for unconstrained multiobjective problems and present a trust-region method to solve it. Under certain assumptions, which are derived in a very natural way from assumptions used to establish convergence results of the scalar trust-region method, we prove that our trust-region method generates a sequence which converges in the Pareto critical way. This means that our generalized marginal function, which generalizes the norm of the gradient for the multiobjective case, converges to zero. In the last section of this paper, we give an application to satisficing processes in Behavioral Sciences. Multiobjective trust-region methods appear to be remarkable specimens of much more abstract satisficing processes, based on 'variational rationality' concepts. One of their important merits is to allow for efficient computations. This is a striking result in Behavioral Sciences. [ABSTRACT FROM AUTHOR]

This article provides the editorial policy of the "Journal of Optimization Theory and Applications." The journal publishes carefully selected papers covering mathematical optimization techniques and their applications to science and engineering. And it issues five types of contributions such as Survey Papers, Contributed Papers, and Technical Notes. Manuscripts, in triplicate, may be submitted to any of the Associate Editors or the Editor-in-Chief.

This paper deals with the time-optimal control problem for a class of fractional order systems. An analytic solution of the time-optimal problem is proposed, and the optimal transfer route is provided. Considering it is usually adopted in the discrete situation for actual control system, the sampling date may induce chattering phenomenon, an alternative sub-optimal solution is constructed. Additionally, the special and meaningful application of fractional order tracking differentiator is introduced to explain our main results. The effectiveness and advantages of the proposed method have been illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

This work can be seen as a sequel to our previous paper, which dealt with local nonlinear error bounds for lower semicontinuous functions on complete metric spaces, based on estimates of the strong slope of the function through the distance to a sublevel set. Here, we consider estimates of the strong slope through the values of the function, and we provide characterizations of nonlinear local and global error bounds that are again obtained by a reduction to the linear case. Our main tool is a simple chain rule for the strong slope. We provide several examples showing that recent results in the literature can be recaptured from our general framework. [ABSTRACT FROM AUTHOR]

The Bregman-function-based Proximal Point Algorithm for variational inequalities is studied. Classical papers on this method deal with the assumption that the operator of the variational inequality is monotone. Motivated by the fact that this assumption can be considered to be restrictive, e.g., in the discussion of Nash equilibrium problems, the main objective of the present paper is to provide a convergence analysis only using a weaker assumption called quasimonotonicity. To the best of our knowledge, this is the first algorithm established for this general and frequently studied class of problems. [ABSTRACT FROM AUTHOR]

This paper deals with a parametric family of convex semi-infinite optimization problems for which linear perturbations of the objective function and continuous perturbations of the right-hand side of the constraint system are allowed. In this context, Cánovas et al. (SIAM J. Optim. 18:717–732, []) introduced a sufficient condition (called ENC in the present paper) for the strong Lipschitz stability of the optimal set mapping. Now, we show that ENC also entails high stability for the minimal subsets of indices involved in the KKT conditions, yielding a nice behavior not only for the optimal set mapping, but also for its inverse. Roughly speaking, points near optimal solutions are optimal for proximal parameters. In particular, this fact leads us to a remarkable simplification of a certain expression for the (metric) regularity modulus given in Cánovas et al. (J. Glob. Optim. 41:1–13, []) (and based on Ioffe (Usp. Mat. Nauk 55(3):103–162, []; Control Cybern. 32:543–554, [])), which provides a key step in further research oriented to find more computable expressions of this regularity modulus. [ABSTRACT FROM AUTHOR]

This paper deals with the class of continuous-time singular linear systems with random abrupt changes. The state feedback stabilization and its robustness for this class of systems with norm-bounded uncertainties are tackled. Sufficient conditions for designing either a stabilizing controller or a robust stabilizing controller are developed in the LMI setting. The developed sufficient conditions are used to synthesize the state feedback controller that guarantees that either the nominal system or the uncertain system is piecewise regular, impulse free and stochastically stable or robust stochastically stable. [ABSTRACT FROM AUTHOR]

In this paper, we establish existence theorems for bilevel problems with fixed-point constraints and bilevel problems without fixed-point constraint. The aim of this paper is to investigate under which conditions the existence of a feasible point of a bilevel problem can be assumed in advance and under which conditions there exist minimizers for this type of problems. From this, we establish existence theorems for mathematical programs with equilibrium constraints and semi-infinite problems. [ABSTRACT FROM AUTHOR]

This paper deals with optimal control problems described by higher index DAEs. We introduce a class of problems which can be transformed to index one control problems. For these problems we show in the accompanying paper that, if the solutions to the adjoint equations are well-defined, then the first-order approximations to the functionals defining the problem can be expressed in terms of the adjoint variables. In this paper we show that the solutions to the adjoint equations are essentially bounded measurable functions. Then, based on the first order approximations, we derive the necessary optimality conditions for the considered class of control problems. These conditions do not require the transformation of the DAEs to index-one system; however, higher-index DAEs and their associated adjoint equations have to be solved. [ABSTRACT FROM AUTHOR]

This paper focuses on a class of discrete-time interconnected pendulumlike systems. Sufficient conditions for the global convergence of systems with both structured and unstructured uncertainties in its linear part are established in terms of linear matrix inequalities (LMIs). In the traditional decentralized control of large scale systems, the effects of interconnections were seldom studied. In this paper, a square matrix specifying the interconnecting structure is introduced in order to discuss the effects of nonlinear interconnections. It is shown that the global convergence of the whole interconnected system can be achieved by designing an appropriate interconnection matrix. In order to solve the nonlinear matrix inequalities (NMIs) arising in the synthesis problem, a global optimization algorithm is presented which can be used to handle a class of NMI problems. An illustrative example is given to demonstrate the applicability and validity of the main results and the presented algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes several globally convergent geometric optimization algorithms on Riemannian manifolds, which extend some existing geometric optimization techniques. Since any set of smooth constraints in the Euclidean space Rn (corresponding to constrained optimization) and the Rn space itself (corresponding to unconstrained optimization) are both special Riemannian manifolds, and since these algorithms are developed on general Riemannian manifolds, the techniques discussed in this paper provide a uniform framework for constrained and unconstrained optimization problems. Unlike some earlier works, the new algorithms have less restrictions in both convergence results and in practice. For example, global minimization in the one-dimensional search is not required. All the algorithms addressed in this paper are globally convergent. For some special Riemannian manifold other than Rn, the newalgorithms are very efficient. Convergence rates are obtained. Applications are discussed. [ABSTRACT FROM AUTHOR]

We present a new duality theory to treat convex optimization problems and we prove that the geometric duality used by Scott and Jefferson in different papers during the last quarter of century is a special case of it. Moreover, weaker sufficient conditions to achieve strong duality are considered and optimality conditions are derived. Next, we apply our approach to some problems considered by Scott and Jefferson, determining their duals. We give weaker sufficient conditions to achieve strong duality and the corresponding optimality conditions. Finally, posynomial geometric programming is viewed also as a particular case of the duality approach that we present. [ABSTRACT FROM AUTHOR]

Ordinal optimization is a tool to reduce the computational burden in simulation-based optimization problems. So far, the major effort in this field focuses on single-objective optimization. In this paper, we extend this to multiobjective optimization and develop vector ordinal optimization, which is different from the one introduced in Ref 1. Alignment probability and ordered performance curve (OPC) are redefined for multiobjective optimization. Our results lead to quantifiable subset selection sizes in the multiobjective case, which supplies guidance in solving practical problems, as demonstrated by the examples in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we continue the analysis of the image regularity condition (IRC) as introduced in a previous paper where we have proved the IRC implies the existence of generalized Lagrange-John multipliers with first component equal to 1. The term generalized is connected with the fact that the separation (in the image space) is not necessarily linear (when we have classic Lagrange-John multipliers), but it can also nonlinear. Here, we prove that the IRC guarantees, also in the nondifferentiable case, the fact that 0 is a solution of the first-order homogeneized (linearized) problem obtained by means of the Dini-Hadamard derivatives. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new predictor-corrector interior-point algorithm for linear programming based on a wide neighbourhood. In each iteration, the algorithm computes the Ai-Zhang's predictor direction (SIAM J. Optim. 16(2):400-417, ) and a new corrector direction, in an attempt to improve its performance. We drive that the duality gap reduces in both predictor and corrector steps. Moreover, we also prove that the complexity of the algorithm coincides with the best iteration bound for small neighbourhood algorithms. Finally, some numerical experiments are provided which reveal capability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Provides information about the "Journal of Optimization Theory and Applications." Types of papers that are published in the journal; Submission guidelines; Page charges; Availability of reprints to authors.

Mathematical analysis and numerical solutions of problems with unknown shapes or geometrical domains is a challenging and rich research field in the modern theory of the calculus of variations, partial differential equations, differential geometry as well as in numerical analysis. In this series of three review papers, we describe some aspects of numerical solution for problems with unknown shapes, which use tools of asymptotic analysis with respect to small defects or imperfections to obtain sensitivity of shape functionals. In classical numerical shape optimization, the boundary variation technique is used with a view to applying the gradient or Newton-type algorithms. Shape sensitivity analysis is performed by using the velocity method. In general, the continuous shape gradient and the symmetric part of the shape Hessian are discretized. Such an approach leads to local solutions, which satisfy the necessary optimality conditions in a class of domains defined in fact by the initial guess. A more general framework of shape sensitivity analysis is required when solving topology optimization problems. A possible approach is asymptotic analysis in singularly perturbed geometrical domains. In such a framework, approximations of solutions to boundary value problems (BVPs) in domains with small defects or imperfections are constructed, for instance by the method of matched asymptotic expansions. The approximate solutions are employed to evaluate shape functionals, and as a result topological derivatives of functionals are obtained. In particular, the topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, cavities, inclusions, defects, source terms and cracks. This new concept of variation has applications in many related fields, such as shape and topology optimization, inverse problems, image processing, multiscale material design and mechanical modeling involving damage and fracture evolution phenomena. In the first part of this review, the topological derivative concept is presented in detail within the framework of the domain decomposition technique. Such an approach is constructive, for example, for coupled models in multiphysics as well as for contact problems in elasticity. In the second and third parts, we describe the first- and second-order numerical methods of shape and topology optimization for elliptic BVPs, together with a portfolio of applications and numerical examples in all the above-mentioned areas. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the inequality constrained vector problem with continuously Fréchet differentiable objective functions and constraints. We obtain second-order necessary optimality conditions of Karush-Kuhn-Tucker type for weak efficiency. A new second-order constraint qualification of Zangwill type is introduced. It is applied in the optimality conditions. Some connections with other constraint qualifications are established. [ABSTRACT FROM AUTHOR]

This paper deals with equilibrium problems with nonlinear constraints. Exploiting a gap function which relies on a polyhedral approximation of the feasible region, we propose two descent methods. They are both based on the minimization of a suitable exact penalty function, but they use different rules for updating the penalization parameter and they rely on different types of line search. The convergence of both algorithms is proved under standard assumptions. [ABSTRACT FROM AUTHOR]

In this paper, we consider a dynamic optimization problem involving a general switched system that evolves by switching between several subsystems of nonlinear delay-differential equations. The optimization variables in this system consist of: (1) the times at which the subsystem switches occur; and (2) a set of system parameters that influence the subsystem dynamics. We first establish the existence of the partial derivatives of the system state with respect to both the switching times and the system parameters. Then, on the basis of this result, we show that the gradient of the cost function can be computed by solving the state system forward in time followed by a costate system backward in time. This gradient computation procedure can be combined with any gradient-based optimization method to determine the optimal switching times and parameters. We propose an effective optimization algorithm based on this idea. Finally, we consider three numerical examples, one involving the 1,3-propanediol fed-batch production process, to illustrate the effectiveness and applicability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The zero propellant maneuver (ZPM) is an advanced space station, large angle attitude maneuver technique, using only control momentum gyroscopes (CMGs). Path planning is the key to success, and this paper studies the associated multi-objective optimization problem. Three types of maneuver optimal control problem are formulated: (i) momentum-optimal, (ii) time-optimal, and (iii) energy-optimal. A sensitivity analysis approach is used to study the Pareto optimal front and allows the tradeoffs between the performance indices to be investigated. For example, it is proved that the minimum peak momentum decreases as the maneuver time increases, and the minimum maneuver energy decreases if a larger momentum is available from the CMGs. The analysis is verified and complemented by the numerical computations. Among the three types of ZPM paths, the momentum-optimal solution and the time-optimal solution generally possess the same structure, and they are singular. The energy-optimal solution saves significant energy, while generally maintaining a smooth control profile. [ABSTRACT FROM AUTHOR]

In this paper, we pursue two goals. First, we find exact relationships between the three concepts of semismooth sets, functions, and maps. Then, we consider the nonsmooth calculus of these notions. Particularly, we prove that the Mordukhovich and linear subdifferentials (coderivatives) are equal for the semismooth functions (maps). Several examples are presented to illustrate the results of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of a solution for a hemivariational inequality problem in a noncoercive framework. The approach adopted is an equilibrium problem formulation associated with a maximal monotone bifunction with pseudomonotone perturbation. We proceed by introducing auxiliary problems that will be studied using a new existence result for equilibrium problems. An example to illustrate the use of the theory is given. [ABSTRACT FROM AUTHOR]

The aim of this paper is to provide a survey of some recent results in the field of optimality conditions in vector optimization with geometric and inequality/equality constraints. Moreover, the discussion we initiate leads us to consider new situations which were not previously studied. [ABSTRACT FROM AUTHOR]

In this paper, we address the stable numerical solution of ill-posed nonlinear least-squares problems with small residual. We propose an elliptical trust-region reformulation of a Levenberg-Marquardt procedure. Thanks to an appropriate choice of the trust-region radius, the proposed procedure guarantees an automatic choice of the free regularization parameters that, together with a suitable stopping criterion, ensures regularizing properties to the method. Specifically, the proposed procedure generates a sequence that even in case of noisy data has the potential to approach a solution of the unperturbed problem. The case of constrained problems is considered, too. The effectiveness of the procedure is shown on several examples of ill-posed least-squares problems. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of solutions for the minimization problem of the shell weight for a given minimal frequency of the shell vibrations as well as for the maximization problem of the minimal frequency for a given shell weight. We consider an optimal control problem governed by an eigenvalue problem for a system of differential equations with variable coefficients. The form of the shell is considered as a control. Some of the coefficients are non-measurable. Earlier, we introduced certain special weighted functional spaces. By using these spaces, we establish the continuity of the considered minimal frequency functional and obtain the existence of solutions of both optimal control problems. At the end, we prove the Lipschitz continuity of the eigenvalue problem. [ABSTRACT FROM AUTHOR]

The batched greedy strategy is an approximation algorithm to maximize a set function subject to a matroid constraint. Starting with the empty set, the batched greedy strategy iteratively adds to the current solution set a batch of elements that results in the largest gain in the objective function while satisfying the matroid constraints. In this paper, we develop bounds on the performance of the batched greedy strategy relative to the optimal strategy in terms of a parameter called the total batched curvature. We show that when the objective function is a polymatroid set function, the batched greedy strategy satisfies a harmonic bound for a general matroid constraint and an exponential bound for a uniform matroid constraint, both in terms of the total batched curvature. We also study the behavior of the bounds as functions of the batch size. Specifically, we prove that the harmonic bound for a general matroid is nondecreasing in the batch size and the exponential bound for a uniform matroid is nondecreasing in the batch size under the condition that the batch size divides the rank of the uniform matroid. Finally, we illustrate our results by considering a task scheduling problem and an adaptive sensing problem. [ABSTRACT FROM AUTHOR]

An optimal control problem governed by a class of semilinear elliptic equations is considered in this paper. Using relaxed controls, the nonexistence and existence results of an optimal control are obtained. [ABSTRACT FROM AUTHOR]

The paper is concerned with the optimistic formulation of a bilevel optimization problem with multiobjective lower-level problem. Considering the scalarization approach for the multiobjective program, we transform our problem into a scalar-objective optimization problem with inequality constraints by means of the well-known optimal value reformulation. Completely detailed first-order necessary optimality conditions are then derived in the smooth and nonsmooth settings while using the generalized differentiation calculus of Mordukhovich. Our approach is different from the one previously used in the literature and the conditions obtained are new. Furthermore, they reduce to those of a usual bilevel program, if the lower-level objective function becomes single-valued. [ABSTRACT FROM AUTHOR]

This paper studies the investment in a group with stickiness. A group investment game is constructed. By analyzing the best response of each player, the equilibria are presented. Furthermore, the convergence region of each equilibrium is outlined, and the sensitivity analysis of the region to parameters is explored. The game with two players is given to illustrate the convergence region of each equilibrium. The explanation and illustration of the results are summarized. The findings indicate that a successful investment usually occurs in a group with 'tolerance', 'open-sharing', 'efficiency', 'sensitivity', and with large members. [ABSTRACT FROM AUTHOR]

In this paper, we study a new system of generalized mixed equilibrium problems involving nonmonotone set-valued mappings and nondifferential bifunctions in Banach spaces. First, a system of auxiliary generalized mixed equilibrium problems are introduced. By using a minimax inequality, the existence and uniqueness of solutions of the system of auxiliary generalized mixed equilibrium problems is proved. Next, by using the auxiliary principle technique, an iterative algorithm for solving the system of generalized mixed equilibrium problems is constructed. Finally, the existence of solutions and the convergence of iterative sequences generated by the algorithm are proved under suitable conditions. These results improve, unify, and generalize many corresponding known results given in literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish theorems of the alternative for inequality systems of real polynomials. For the real quadratic inequality system, we present two new results on the matrix decomposition, by which we establish two theorems of the alternative for the inequality system of three quadratic polynomials under an assumption that at least one of the involved forms be negative semidefinite. We also extend a theorem of the alternative to the case with a regular cone. For the inequality system of higher degree real polynomials, defined by even order tensors, a theorem of the alternative for the inequality system of two higher degree polynomials is established under suitable assumptions. As a byproduct, we give an equivalence result between two statements involving two higher degree polynomials. Based on this result, we investigate the optimality condition of a class of polynomial optimization problems under suitable assumptions. [ABSTRACT FROM AUTHOR]

Due to its significant efficiency, the alternating direction method (ADM) has attracted a lot of attention in solving linearly constrained structured convex optimization. In this paper, in order to make implementation of ADM relatively easy, some linearized proximal ADMs are proposed and the associated convergence results of the proposed linearized proximal ADMs are given. Additionally, theoretical analysis shows that the relaxation factor for the linearized proximal ADMs can have the same restriction region as that for the general ADM. [ABSTRACT FROM AUTHOR]

In this paper, the problem of passivity analysis is investigated for stochastic interval neural networks with interval time-varying delays and Markovian jumping parameters. By constructing a proper Lyapunov-Krasovskii functional, utilizing the free-weighting matrix method and some stochastic analysis techniques, we deduce new delay-dependent sufficient conditions, that ensure the passivity of the proposed model. These sufficient conditions are computationally efficient and they can be solved numerically by linear matrix inequality (LMI) Toolbox in Matlab. Finally, numerical examples are given to verify the effectiveness and the applicability of the proposed results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider a class of nondifferentiable multiobjective fractional programming problems in which every component of the objective function contains a term involving the support function of a compact convex set. Based on the ( C, α, ρ, d)-convexity, sufficient optimality conditions and duality results for weakly efficient solutions of the nondifferentiable multiobjective fractional programming problem are established. The results extend and improve the corresponding results in the literature. [ABSTRACT FROM AUTHOR]