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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.

Provides information about the book "Journal of Optimization Theory and Applications." Editorial policy; Preparation of papers; Editorial addresses.

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 the present paper, we analyze a class of convex semi-infinite programming problems with arbitrary index sets defined by a finite number of nonlinear inequalities. The analysis is carried out by employing the constructive approach, which, in turn, relies on the notions of immobile indices and their immobility orders. Our previous work showcasing this approach includes a number of papers dealing with simpler cases of semi-infinite problems than the ones under consideration here. Key findings of the paper include the formulation and the proof of implicit and explicit optimality conditions under assumptions, which are less restrictive than the constraint qualifications traditionally used. In this perspective, the optimality conditions in question are also compared to those provided in the relevant literature. Finally, the way to formulate the obtained optimality conditions is demonstrated by applying the results of the paper to some special cases of the convex semi-infinite problems. [ABSTRACT FROM AUTHOR]

The paper presents results of CFD parametric study of centrifugal compressor stage vane diffusers in the Ansys CFX. The results obtained will be used to build a mathematical model of vane diffuser in optimization design system. Objects of research are vane diffusers with external relative diameter (relative to the diameter of the impeller) equal to 1.5; vane inlet angle of 20°; relative vane heights of 0.025, 0.034, 0.045, 0.06, and 0.08; and vane profile curvature angles of 10, 15, and 20 °. The characteristics of polytrophic efficiency, loss coefficient, recovery coefficient, ratio of inlet and outlet velocities, and flow deviation angle versus incidence angle are set. The analysis of the flow structure in the vane diffuser channels is presented. Unlike with a straight vane cascade, the deviation angle in the circular rows of vane diffusers tends to increase with increasing row density. This may be due to the complex nature of the interaction of the active part of the flow with separation zones. In rows with almost straight vanes at a lower density, the separation zone on the pressure side decreases and even shifts to the very end of the suction side. [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]

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 this note, with reference to a paper by the same authors, we add an extra assumption, correct the statement of Lemma 2.1 and subsequently correct the proof of this lemma. [ABSTRACT FROM AUTHOR]

The present paper studies a new class of problems of optimal control theory with Sturm-Liouville-type differential inclusions involving second-order linear self-adjoint differential operators. Our main goal is to derive the optimality conditions of Mayer problem for differential inclusions with initial point constraints. By using the discretization method guaranteeing transition to continuous problem, the discrete and discrete-approximation inclusions are investigated. Necessary and sufficient conditions, containing both the Euler-Lagrange and Hamiltonian-type inclusions and “transversality” conditions are derived. The idea for obtaining optimality conditions of Mayer problem is based on applying locally adjoint mappings. This approach provides several important equivalence results concerning locally adjoint mappings to Sturm-Liouville-type set-valued mappings. The result strengthens and generalizes to the problem with a second-order non-self-adjoint differential operator; a suitable choice of coefficients then transforms this operator to the desired Sturm-Liouville-type problem. In particular, if a positive-valued, scalar function specific to Sturm-Liouville differential inclusions is identically equal to one, we have immediately the optimality conditions for the second-order discrete and differential inclusions. Furthermore, practical applications of these results are demonstrated by optimization of some “linear” optimal control problems for which the Weierstrass-Pontryagin maximum condition is obtained. [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.

We present convergence and error estimates of modified versions of the time-discrete consensus-based optimization (CBO) algorithm proposed in Carrillo et al. (ESAIM: Control Optim Calc Var, 2020) for general non-convex functions. In authors' recent work (Ha et al. in Math Models Meth Appl Sci 30:2417–2444, 2020), rigorous error analysis of a modified version of the first-order consensus-based optimization algorithm proposed in Carrillo et al. (2020) was studied at the particle level without resorting to the kinetic equation via a mean-field limit. However, the error analysis for the corresponding time- discrete algorithm was not done mainly due to lack of discrete analogue of Itô's stochastic calculus. In this paper, we provide a simple and elementary convergence and error analysis for a general time-discrete consensus-based optimization algorithm, which includes modifications of the three discrete algorithms in Carrillo et al. (2020), two of which are present in Ha et al. (2020). Our analysis provides numerical stability and convergence conditions for the three algorithms, as well as error estimates to the global minimum. [ABSTRACT FROM AUTHOR]

The aim of this paper is twofold. It introduces a theory of Michell trusses taking support (reaction) costs into consideration, which is illustrated with a modified version of Michell's best known example. Then eight other variations on this example are presented, with (i) equal or unequal permissible stresses in tension and compression, (ii) the structural domain consisting of a half-plane or a full plane, and (iii) the supports being two pins, or a pin and a roller. Previously noted shortcomings of Michell's theory are highlighted and several fundamental properties of non-selfadjoint topology optimization problems discussed. The analytical solutions are verified to a high degree of accuracy by numerical results. [ABSTRACT FROM AUTHOR]

The dynamical systems approach to sizing and SIMP topology optimization, introduced in a previous paper, is extended to the case of time-varying loads. A general dynamical system, satisfying a Lyaponov-type descent condition, is derived and specialized to a goal function combining stiffness and mass. For a cyclic time-dependent load it is indicated how, in the limit of short cycles compared to the overall time scale, this can be handled by multiple load cases. Numerical examples, both for a convex and a non-convex case, illustrates the theory. [ABSTRACT FROM AUTHOR]

This paper deals with topology optimization based on the Heaviside projection method using a scalar function as design variables. The scalar function is then regularized by a PDE based filter. Several image-processing based filtering techniques have so far been proposed for regularization or restricting the minimum length scale. They are conventionally applied to the design sensitivities rather than the design variables themselves. However, it causes discrepancies between the filtered sensitivities and the actual sensitivities that may confuse the optimization process and disturb the convergence. In this paper, we propose a Heaviside projection based topology optimization method with a scalar function that is filtered by a Helmholtz type partial differential equation. Therefore, the optimality can be strictly discussed in terms of the KKT condition. In order to demonstrate the effectiveness of the proposed method, a minimum compliance problem is solved. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with the problem of unboundedness and existence of an optimal solution in reverse convex and concave integer optimization problems. In particular, we present necessary and sufficient conditions for existence of an upper bound for a convex objective function defined over the feasible region contained in $${\mathbb{Z}^n}$$. The conditions for boundedness are provided in a form of an implementable algorithm, showing that for the considered class of functions, the integer programming problem is unbounded if and only if the associated continuous problem is unbounded. We also address the problem of boundedness in the global optimization problem of maximizing a convex function over a set of integers contained in a convex and unbounded region. It is shown in the paper that in both types of integer programming problems, the objective function is either unbounded from above, or it attains its maximum at a feasible integer point. [ABSTRACT FROM AUTHOR]

In this paper, we consider approximation algorithms for optimizing a generic multi-variate homogeneous polynomial function, subject to homogeneous quadratic constraints. Such optimization models have wide applications, e.g., in signal processing, magnetic resonance imaging (MRI), data training, approximation theory, and portfolio selection. Since polynomial functions are non-convex, the problems under consideration are all NP-hard in general. In this paper we shall focus on polynomial-time approximation algorithms. In particular, we first study optimization of a multi-linear tensor function over the Cartesian product of spheres. We shall propose approximation algorithms for such problem and derive worst-case performance ratios, which are shown to be dependent only on the dimensions of the model. The methods are then extended to optimize a generic multi-variate homogeneous polynomial function with spherical constraint. Likewise, approximation algorithms are proposed with provable approximation performance ratios. Furthermore, the constraint set is relaxed to be an intersection of co-centered ellipsoids; namely, we consider maximization of a homogeneous polynomial over the intersection of ellipsoids centered at the origin, and propose polynomial-time approximation algorithms with provable worst-case performance ratios. Numerical results are reported, illustrating the effectiveness of the approximation algorithms studied. [ABSTRACT FROM AUTHOR]

The article introduces the special issue of "Mathematical Programming, Series B," with topics including continuous optimization.

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 multicriteria discrete-continuous problems of scheduling nonpreemptable jobs. The need for reusability and modularity leads us to build a “generic” optimisation and simulation framework, while the need to quickly generate good compromises between conflicting objectives requires the implementation of multicriteria scheduling models. This paper describes the practical possibilities of three hybrid models within this framework. The validation of the framework is presented in terms of its application to a real, highly constrained, discrete-continuous problem. The optimisation model is based on the hybridisation of a classical hill-climber meta-heuristic with the Promethee II multicriteria method. [ABSTRACT FROM AUTHOR]

Abstract??The paper considers the problem of finding a spanning arborescence on a directed network whose arc costs are partially known. It is assumed that each arc cost can take on values from a known interval defining a possible economic scenario. In this context, the problem of finding the spanning arborescence whichbetterapproaches to that of minimum overall cost under each possible scenario is studied. The minimax regret criterion is proposed in order to obtain such a robust solution of the problem. As it is shown, the bounds on the optimal value of the minimax regret optimization problem obtained in a previous paper, can be used here in a Branch and Bound algorithm in order to give an optimal solution. The computational behavior of the algorithm is tested through numerical experiments. [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]

In a recent paper [Int J Game Theory (2001) 30:99-106], Chu and Halpern investigated the problem of finding optimal strategies in certain games with common payoffs. This short technical note answers a computational complexity question that was left open in their paper. [ABSTRACT FROM AUTHOR]

In this paper, a new multi-objective uniform-diversity differential evolution (MUDE) algorithm is proposed and used for Pareto optimum design of mechanisms. The proposed algorithm uses a diversity preserving mechanism called the ε-elimination algorithm to improve the population diversity among the obtained Pareto front. The proposed algorithm is firstly tested on some constrained and unconstrained benchmarks proposed for the special session and competition on multi-objective optimizers held under IEEE CEC 2009. The inverted generational distance (IGD) measure is used to assess the performance of the algorithm. Secondly, the proposed algorithm has been used for multi-objective optimization of two different combinatorial case studies. The first case contains a two-degree of freedom leg mechanism with springs. Three conflicting objective functions that have been considered for Pareto optimization are namely, leg size, vertical actuating force, and the peak crank torque. The second case is a two-finger robot gripper mechanism with two conflicting objectives which are the difference between the maximum and minimum gripping force and the transmission ratio of actuated and experienced gripper forces. Comparisons of obtained Pareto fronts using the method of this work with those obtained in other references show significant improvements. [ABSTRACT FROM AUTHOR]

In this paper, multi-objective particle swarm optimization with preference information (MOPSO-PI) has been proposed. In the proposed algorithm, the information entropy is employed for measuring the probability distribution of particles; the user's preference information is represented as the ranking of each particle through the possible matrix. The optimal procedure is guided by the preference information since the global best performance of particle is randomly chosen among non-dominated solutions with higher ranking value in each iteration. Finally, the MOPSO-PI is applied to optimize the steelmaking process; the power supply curve obtained reduces the electric energy consumption, shortens the smelting time and prolongs the lifespan of the furnace lining. The application results show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Plates with ribs or stiffeners (stiffened plates) have been widely used as primary or secondary load bearing structures. Such structures could be fabricated by casting - a conventional yet important manufacturing process, their load bearing capacities are strongly dependent on the layout and sizes of the stiffeners. Thus it is necessary to establish specific topology optimization model and algorithm to obtain optimum layout, sizes and shapes of the stiffeners with casting constraints being considered. In this paper, we propose a new Heaviside-function based directional growth topology parameterization (H-DGTP) of the casting constraints for simultaneously optimizing the layout and height of the stiffeners. By using the new explicit parameterization, we can obtain a clear stiffener layout with optimized height. The differentiability of the parameterization is obtained by the use of a smooth approximation of the Heaviside function. In order to be applicable to a non-uniform mesh, a base surface is introduced and the minimum length of a stiffener can be controlled. Several numerical examples are presented to show the validity of this method. [ABSTRACT FROM AUTHOR]

The paper concerns worst-case compliance optimization by finding the structural topology with minimum compliance for the loading due to the worst possible acceleration of the structure and attached non-structural masses. A main novelty of the paper is that it is shown how this min-max problem can be formulated as a non-linear semi-definite programming (SDP) problem involving a small-size constraint matrix and how this problem is solved numerically. Our SDP formulation is an extension of an eigenvalue problem seen previously in the literature; however, multiple eigenvalues naturally arise which makes the eigenvalue problem non-smooth, whereas the SDP problem presented in this paper provides a computationally tractable problem. Optimized designs, where the uncertain loading is due to acceleration of applied masses and the weight of the structure itself, are shown in two and three dimensions and we show that these designs satisfy optimality conditions that are also presented. [ABSTRACT FROM AUTHOR]

Optimal blank shape minimizing earing in deep drawing has a direct influence on material saving as well as product quality. A number of methods for blank shape optimization have been previously proposed, most of which adopt a closed-loop type algorithm that requires a large number of simulation runs. Numerical simulation in sheet metal forming is so numerically intensive that it is preferable to find an optimal blank shape with a small number of simulation runs. This paper proposes a method for determining the optimal blank shape design in square cup deep drawing using sequential approximate optimization (SAO) with a radial basis function (RBF) network. Sheet metal forming is multi-objective in nature, and thus the blank shape design problem is formulated as a multi-objective design optimization. The aim is therefore to identify the pareto-frontier with a small number of simulation runs. The earing is minimized under tearing and wrinkling constraints with a variable blank holder force (VBHF), which varies through the punch stroke. Numerical results show that the disconnected pareto-frontier is well identified with a small number of simulation runs. The earing of the optimal blank shape with the VBHF is also drastically reduced, when compared to a reference blank shape. Based on the numerical results, the experiments using a servo press are carried out. Consequently, the validity of the proposed approach is confirmed through the numerical and experimental results. [ABSTRACT FROM AUTHOR]

This paper presents a surrogate constraint tabu thresholding (SCTT) implementation for solving the frequency assignment problem. The frequency assignment problem is an important combinatorial optimisation problem that arises in telecommunications. The main objective is to assign radio frequencies to a number of communication links such that interference is minimised. Interference is minimised by satisfying a number of problem specific constraints. The surrogate constraint is created by taking a weighted sum of the constraints not satisfied. SCTT is compared with a tabu thresholding method from the literature on a set of simulated but realistic test problems with respect to quality of the solution in a given time period. Computational results show that SCTT is more efficient and effective for all the test problems. [ABSTRACT FROM AUTHOR]

In formulating a combinatorial optimisation problem (COP) using Discrete or Integer Programming (IP) modelling techniques, the modeller is restricted to use only certain predefined discrete variables and sets which are linked by sets of linear equality and inequality constraints. Definition of many COPs includes restrictions in which the use of dis-equality (DI) constraints in their mathematical representation is inevitable. To represent this type of constraint a number of binary variables and extra constraints are usually introduced, which lead to an increase in the size of the model in terms of variables and constraints. In this paper, we introduce a new class of discrete variables which enables the modeller to represent DI constraints more efficiently in the mathematical formulation of a combinatorial optimisation problem. We have also introduced a new branching scheme to the conventional simplex based Branch and Bound (B&B) algorithm in order to deal with this type of variables. To study the effect of these variables, we modelled and solved a set of five classic problems, first using conventional MP variables and second, exploiting the new proposed variables, and compared the results. The empirical results show a promising improvement on the performance of the B&B algorithm. The contribution of this paper is (1) the introduction of a new class of discrete variables which can help to build smaller models, and (2) new branching schemes on these variables that can improve the B&B performance. [ABSTRACT FROM AUTHOR]

This paper explores the use of simulated annealing (SA) for solving arbitrary combinatorial optimisation problems. It reviews an existing code called GPSIMAN for solving 0–1 problems, and evaluates it against a commercial branch-and-bound code, OSL. The problems tested include travelling salesman, graph colouring, bin packing, quadratic assignment and generalised assignment. The paper then describes a technique for representing these problems using arbitrary integer variables, and shows how a general simulated annealing algorithm can also be applied. This new code, INTSA, outperforms GPSIMAN and OSL on almost all of the problems tested. [ABSTRACT FROM AUTHOR]

This paper presents a special class of equilibria in finite strategy noncooperative games, which are extensions of the traditional Nash equilibrium solution. An underlying role in these equilibria play the assumed extended models of players' rationality principles which admit their non-myopic behaviour. The crucial idea is that players possessing some information about their opponents and the game itself can forecast the consequences of their choices by analyzing the ‘move-countermove’ possible sequences and accordingly predict the stability of game outcomes. The class of discussed equilibria besides the classical Nash equilibrium includes all the solutions considered in metagame and hypergame theories, and its determinants allow for a useful characterization of new potential equilibria concepts in modeled real-life conflicts. For specific equilibrium concepts, their individual properties are discussed and some analytical characterizations are provided. The paper concludes with the description of a computer-based procedure developed for calculating different kinds of generalized equilibrium points. Possible applications of this procedure within simulation and gaming are briefly discussed. [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 proposes a mechanism to produce equivalent Lipschitz surrogates for zero-norm and rank optimization problems by means of the global exact penalty for their equivalent mathematical programs with an equilibrium constraint (MPECs). Specifically, we reformulate these combinatorial problems as equivalent MPECs by the variational characterization of the zero-norm and rank function, show that their penalized problems, yielded by moving the equilibrium constraint into the objective, are the global exact penalization, and obtain the equivalent Lipschitz surrogates by eliminating the dual variable in the global exact penalty. These surrogates, including the popular SCAD function in statistics, are also difference of two convex functions (D.C.) if the function and constraint set involved in zero-norm and rank optimization problems are convex. We illustrate an application by designing a multi-stage convex relaxation approach to the rank plus zero-norm regularized minimization problem. [ABSTRACT FROM AUTHOR]

A chance constrained optimization problem over a finite distribution involves a set of scenario constraints from which a small subset can be violated. We consider the setting where all scenario constraints are mixed-integer convex. Existing works typically consider a mixed integer nonlinear programming (MINLP) formulation of this problem by introducing binary variables to indicate which constraint systems are to be satisfied or violated. A variety of cutting plane approaches for this MINLP formulation have been developed. In this paper we consider a family of cuts in the original space rather than those in the extended space of the MINLP reformulation. These cuts, known as quantile cuts, can be viewed as a projection of the well known family of mixing inequalities for the MINLP reformulation onto the original problem space. We show that the closure of the infinite family of all quantile cuts has a finite description. An important corollary of this result is that for linear chance constrained problems the quantile closure is polyhedral. We further show that a recursive application of quantile closure operations recovers the convex hull of the nonconvex chance constrained set in the limit, and in the pure integer setting the convergence is finite. We show that separation of quantile cuts is in general NP-hard, develop a heuristic separation method, and demonstrate its effectiveness through a computational study. We also study an approximation of the quantile closure and propose a generalization by grouping scenarios. [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 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]

In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions. [ABSTRACT FROM AUTHOR]

In 1937, George Pólya wrote what is considered one of the most significant papers in 20th-century mathematics. The article contained one theorem and 100 pages of applications. It introduced a combinatorial method which led to unexpected applications to diverse problems in science like the enumeration of isomers of chemical compounds. Pólya's theory of enumeration was discussed in detail in [1] by Shriya Anand, a summer student of the author. In what follows, we briefly recall the theory and complement the earlier article by adding some other applications not discussed there. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) is the problem of approximating a given nonnegative matrix by the product of two nonnegative matrices. The multiplicative updates proposed by Lee and Seung are widely used as efficient computational methods for NMF. However, the global convergence of these updates is not formally guaranteed because they are not defined for all pairs of nonnegative matrices. In this paper, we consider slightly modified versions of the original multiplicative updates and study their global convergence properties. The only difference between the modified updates and the original ones is that the former do not allow variables to take values less than a user-specified positive constant. Using Zangwill's global convergence theorem, we prove that any sequence of solutions generated by either of those modified updates has at least one convergent subsequence and the limit of any convergent subsequence is a stationary point of the corresponding optimization problem. Furthermore, we propose algorithms based on the modified updates that always stop within a finite number of iterations. [ABSTRACT FROM AUTHOR]

Copositive programming has become a useful tool in dealing with all sorts of optimisation problems. It has however been shown by Murty and Kabadi (Math. Program. 39(2):117-129, ) that the strong membership problem for the copositive cone, that is deciding whether or not a given matrix is in the copositive cone, is a co-NP-complete problem. From this it has long been assumed that this implies that the question of whether or not the strong membership problem for the dual of the copositive cone, the completely positive cone, is also an NP-hard problem. However, the technical details for this have not previously been looked at to confirm that this is true. In this paper it is proven that the strong membership problem for the completely positive cone is indeed NP-hard. Furthermore, it is shown that even the weak membership problems for both of these cones are NP-hard. We also present an alternative proof of the NP-hardness of the strong membership problem for the copositive cone. [ABSTRACT FROM AUTHOR]

In this paper, optimality conditions are presented and analyzed for the cardinality-constrained cone programming arising from finance, statistical regression, signal processing, etc. By introducing a restricted form of (strict) Robinson constraint qualification, the first-order optimality conditions for the cardinality-constrained cone programming are established based upon the properties of the normal cone. After characterizing further the second-order tangent set to the cardinality-constrained system, the second-order optimality conditions are also presented under some mild conditions. These proposed optimality conditions, to some extent, enrich the optimization theory for noncontinuous and nonconvex programming problems. [ABSTRACT FROM AUTHOR]

This paper develops a semi-supervised learning algorithm called convolutional deep networks (CDN), to address the image classification problem with deep learning. First, we construct the previous several hidden layers using convolutional restricted Boltzmann machines, which can reduce the dimension and abstract the information of the images effectively. Second, we construct the following hidden layers using restricted Boltzmann machines, which can abstract the information of images quickly. Third, the constructed deep architecture is fine-tuned by gradient-descent based supervised learning with an exponential loss function. CDN can reduce the dimension and abstract the information of the images at the same time efficiently. More importantly, the abstraction and classification procedure of CDN use the same deep architecture to optimize the same parameter in different steps continuously, which can improve the learning ability effectively. We did several experiments on two standard image datasets, and show that CDN are competitive with both representative semi-supervised classifiers and existing deep learning techniques. [ABSTRACT FROM AUTHOR]

This paper introduces novel numerical solution strategies for generalized semi-infinite optimization problems (GSIP), a class of mathematical optimization problems which occur naturally in the context of design centering problems, robust optimization problems, and many fields of engineering science. GSIPs can be regarded as bilevel optimization problems, where a parametric lower-level maximization problem has to be solved in order to check feasibility of the upper level minimization problem. The current paper discusses several strategies to reformulate this class of problems into equivalent finite minimization problems by exploiting the concept of Wolfe duality for convex lower level problems. Here, the main contribution is the discussion of the non-degeneracy of the corresponding formulations under various assumptions. Finally, these non-degenerate reformulations of the original GSIP allow us to apply standard nonlinear optimization algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose a decentralized parallel computation model for global optimization using interval analysis. The model is adaptive to any number of processors and the workload is automatically and evenly distributed among all processors by alternative message passing. The problems received by each processor are processed based on their local dominance properties, which avoids unnecessary interval evaluations. Further, the problem is treated as a whole at the beginning of computation so that no initial decomposition scheme is required. Numerical experiments indicate that the model works well and is stable with different number of parallel processors, distributes the load evenly among the processors, and provides an impressive speedup, especially when the problem is time-consuming to solve. [ABSTRACT FROM AUTHOR]

This paper presents a convex mathematical programming model for the global optimization of recycle/reuse water networks. The model is based on a general superstructure that includes the major configurations of interest such as segregation, mixing, recycle, bypass, and treatment of streams needed to satisfy the process and environmental constraints. The basic idea of the model formulation is to consider component balances, treating as optimization variables the individual flowrates. This formulation avoids the bilinear terms that appear when the compositions and total flowrates are considered as optimization variables. The objective function consists in the minimization of the total annual cost including the fresh sources costs, the treatment units costs (which are reformulated as convex functions) and the piping costs. Four examples problems are solved to show the applicability of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the stability of the sets of efficient points of vector-valued optimization problems when the data of the approximate problems converges to the data of the original problem in the sense of Painlevé-Kuratowski. Our results improve the corresponding results obtained by Lucchetti and Miglierina (Optimization 53(5-6):517-528, , Section 3). [ABSTRACT FROM AUTHOR]

In this paper we propose a Fully Polynomial Time Approximation Scheme for a class of optimization problems where the feasible region is a polyhedral one and the objective function is the sum or product of ratios of linear functions. The class includes the well known ones of Linear (Sum-of-Ratios) Fractional Programming and Multiplicative Programming. [ABSTRACT FROM AUTHOR]

Genetic algorithms (GAs) can precisely handle the discrete structural topology optimization of single-piece elastic structures called compliant mechanisms. The initial population of these elastic structures is mostly generated by assigning the material at random. This causes disconnected or unfeasible designs and further rule-based repairing can result in representation degeneracy. However, the problem-specific initial population can affect the performance of GAs like other operators. In this paper, a domain-specific initial population strategy is developed that generates geometrically feasible structures for path generating compliant mechanisms (PGCMs). It is coupled with the elitist non-dominated sorting genetic algorithm (NSGA-II) which has been customized for structural topology optimization. The performance of initial population strategy over random initialization using customized NSGA-II is checked on single and bi-objective optimization problems. Based on the results, it is observed that the custom initialization outperforms the random initialization by dominating all the solutions and exploring larger area of posed objectives. The elastic structures obtained by solving two examples of PGCMs using domain specific initial population strategy are also presented. [ABSTRACT FROM AUTHOR]

For 30 years after their invention half a century ago, cutting planes for integer programs have been an object of theoretical investigations that had no apparent practical use. When they finally proved their practical usefulness in the late eighties, that happened in the framework of branch and bound procedures, as an auxiliary tool meant to reduce the number of enumerated nodes. To this day, pure cutting plane methods alone have poor convergence properties and are typically not used in practice. Our reason for studying them is our belief that these negative properties can be understood and thus remedied only based on a thorough investigation of such procedures in their pure form. In this paper, the second in a sequence, we address some important issues arising when designing a computationally sound pure cutting plane method. We analyze the dual cutting plane procedure proposed by Gomory in 1958, which is the first (and most famous) convergent cutting plane method for integer linear programming. We focus on the enumerative nature of this method as evidenced by the relative computational success of its lexicographic version (as documented in our previous paper on the subject), and we propose new versions of Gomory's cutting plane procedure with an improved performance. In particular, the new versions are based on enumerative schemes that treat the objective function implicitly, and redefine the lexicographic order on the fly to mimic a sound branching strategy. Preliminary computational results are reported. [ABSTRACT FROM AUTHOR]

In this paper we discuss domain reduction strategies for global optimization problems with a nonconvex objective function over a bounded convex feasible region. After introducing a standard domain reduction and its iterated version, we will introduce a new reduction strategy. Under mild assumptions, we will prove the equivalence between the new domain reduction and the iterated version of the standard one, allowing a new interpretation of the latter and a new way of computing it. Finally, we prove that any “reasonable” domain reduction strategy is independent of the order by which variables are processed. [ABSTRACT FROM AUTHOR]