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Abstract: In this paper, we introduce and analyze a new hybrid iterative algorithm for finding a common element of the set of solutions of mixed equilibrium problems and the set of fixed points of an infinite family of nonexpansive mappings. Furthermore, we prove some strong convergence theorems for the hybrid iterative algorithm under some mild conditions. We also discuss some special cases. Results obtained in this paper improve the previously known results in this area. [Copyright &y& Elsevier]

Abstract: A shared variable construction is called buffer-based if the values of the variable are stored in buffers that are different from control storage. Each buffer stores only a single value from the domain of the variable. A buffer-based construction is conflict-free if, in each execution of the shared variable, no reading of any buffer overlaps with any writing of that buffer. This paper studies shared space requirements for wait-free, conflict-free, deterministic constructions of 1-writer 1-reader multivalued atomic variables from safe variables. That four buffers are necessary and sufficient for such constructions has been established in the literature. This paper establishes the requirement for control storage. The least shared space for such a construction in the literature is (four safe buffers and) four safe control bits. We show that four safe control bits are necessary for such constructions when the reader is restricted to read at most one buffer in each read operation. [Copyright &y& Elsevier]

Abstract: In this paper, we suggest and analyze a new inexact proximal point method for solving general variational inequalities, which can be considered as an implicit predictor–corrector method. An easily measurable error term is proposed with further relaxed error bound and an optimal step length is obtained by maximizing the profit-function and is dependent on the previous points. Our results include several known and new techniques for solving variational inequalities and related optimization problems. Results obtained in this paper can be viewed as an important improvement and refinement of the previously known results. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: Design of an optimal shock-damping isolator is presented in this paper with specific application to casters. The design is first formulated as an optimization problem to minimize the peak acceleration of a load while keeping the maximal deflection of the isolator within a specified physical limit. The resulting solution is a constant force isolator. However, it is difficult to realize a constant force isolator with conventional mechanisms using linear springs and dampers. To implement such an isolator physically, a novel mechanism employing multiple linear springs has been developed. The structure and the parameters of the springs have been chosen by optimization techniques, and the resulting mechanism has been embodied in a prototype caster design. This paper presents the concept, design procedure, simulation and experimental evaluation results of a prototype optimal shock-damping caster in detail. The peak acceleration of this new design is only 65% of the existing caster. From a manufacturing point of view, this newly designed caster is not much more complex than existing ones. [Copyright &y& Elsevier]

Abstract: In this paper, we describe a numerical approach based on finite difference method to solve a mathematical model arising from a model of neuronal variability. The mathematical modelling of the determination of the expected time for generation of action potentials in nerve cells by random synaptic inputs in dendrites includes a general boundary-value problem for singularly perturbed differential–difference equation with small shifts. In the numerical treatment for such type of boundary-value problems, first we use Taylor approximation to tackle the terms containing small shifts which converts it to a boundary-value problem for singularly perturbed differential equation. A rigorous analysis is carried out to obtain priori estimates on the solution of the problem and its derivatives up to third order. Then a parameter uniform difference scheme is constructed to solve the boundary-value problem so obtained. A parameter uniform error estimate for the numerical scheme so constructed is established. Though the convergence of the difference scheme is almost linear but its beauty is that it converges independently of the singular perturbation parameter, i.e., the numerical scheme converges for each value of the singular perturbation parameter (however small it may be but remains positive). Several test examples are solved to demonstrate the efficiency of the numerical scheme presented in the paper and to show the effect of the small shift on the solution behavior. [Copyright &y& Elsevier]

A novel technique for the multi-parameter optimization of distributed piezoelectric actuators is presented in this paper. The proposed method is designed to improve the performance of multi-mode vibration control in cylindrical shells. The optimization parameters of actuator patch configuration include position, size, and tilt angle. The modal control force of tilted orthotropic piezoelectric actuators is derived and the multi-parameter cylindrical shell optimization model is established. The linear quadratic energy index is employed as the optimization criterion. A geometric constraint is proposed to prevent overlap between tilted actuators, which is plugged into a genetic algorithm to search the optimal configuration parameters. A simply-supported closed cylindrical shell with two actuators serves as a case study. The vibration control efficiencies of various parameter sets are evaluated via frequency response and transient response simulations. The results show that the linear quadratic energy indexes of position and size optimization decreased by 14.0% compared to position optimization; those of position and tilt angle optimization decreased by 16.8%; and those of position, size, and tilt angle optimization decreased by 25.9%. It indicates that, adding configuration optimization parameters is an efficient approach to improving the vibration control performance of piezoelectric actuators on shells. [ABSTRACT FROM AUTHOR]

In this paper we present a strategy for correcting model deficiency using observational data. We first present the model correction in a general form, involving both external correction and internal correction. The model correction problem is then parameterized and casted into an optimization problem, from which the parameters are determined. More importantly, we discuss the incorporation of physical constraints from the underlying physical problem. Several representative examples are presented, where the physical constraints take very different forms. Numerical tests demonstrate that the physics constrained model correction is an effective way to address model-form uncertainty. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we computed all the 379 118 solutions of the equation in distinct odd natural numbers for . We provide a lower bound for the number of solutions of . Also, we answer similar questions about the equation . Finally, we prove some results concerning optimization of and . [Copyright &y& Elsevier]

Abstract: Bauschke, Borwein and Wang have shown in [H.H. Bauschke, J.M. Borwein, X. Wang, Fitzpatrick functions and continuous linear monotone operators, Siam J. Optimization, 18 (3) (2007), 789–809] that if denotes the Fitzpatrick function of a continuous linear monotone operator on a separable real Hilbert space , then , where denotes the Fenchel conjugate of the function sending to for an arbitrary continuous positive symmetric operator . Here, and denotes the Moore–Penrose type inverse of a positive symmetric operator . The main result of the present paper is a sharpening of the result, achieved by showing that and that on , where is the set on which an extended real-valued function is finite. We will also find a formula for the Fitzpatrick function of a general -cyclic monotone linear operator in terms of a corresponding ordinary monotone linear operator. [Copyright &y& Elsevier]

Abstract: In this paper we explain how to characterize the best approximation to any in a Hilbert space from the set in the face of data uncertainty in the convex constraints, , where is a closed convex subset of . Following the robust optimization approach, we establish Lagrange multiplier characterizations of the robust constrained best approximation that is immunized against data uncertainty. This is done by characterizing the best approximation to any from the robust counterpart of the constraints where the constraints are satisfied for all possible uncertainties within the prescribed uncertainty sets. Unlike the traditional Lagrange multiplier characterizations without data uncertainty, for constrained best approximation problems in the face uncertainty, we show that the strong conical hull intersection property (strong CHIP) alone is not sufficient to guarantee the Lagrange multiplier characterizations. We present conditions which guarantee that the strong CHIP is necessary and sufficient for the multiplier characterization. We also establish that the strong CHIP is automatically satisfied for the cases of polyhedral constraints with polytope uncertainty, and linear constraints with interval uncertainty. As an application, we show how robust solutions of shape preserving interpolation problems under ellipsoidal and box uncertainty cases can be obtained in terms of Lagrange multipliers under strict robust feasibility conditions. [Copyright &y& Elsevier]

Abstract: In this paper, we show that the convex optimization problem can be solved by the proximal point algorithm in a finite number of steps under the assumption that the solution set is a set of weak sharp minima. [Copyright &y& Elsevier]

Abstract: In this paper, we use the potential analysis to study the properties of the positive solutions of a γ-Laplace system in Here , satisfy the critical condition . First, the positive solutions u and v satisfy an integral system involving the Wolff potentials. We then use the method of regularity lifting to obtain an optimal integrability for this Wolff type integral system. Different from the case of , it is more difficult to handle the asymptotics since u and v have not radial structures. We overcome this difficulty by a new method and obtain the decay rates of u and v as . We believe that this new method is appropriate to deal with the asymptotics of other decaying solutions without the radial structures. [Copyright &y& Elsevier]

Abstract: The copositive cone, and its dual the completely positive cone, have useful applications in optimisation, however telling if a general matrix is in the copositive cone is a co-NP-complete problem. In this paper we analyse some of the geometry of these cones. We discuss a way of representing all the maximal faces of the copositive cone along with a simple equation for the dimension of each one. In doing this we show that the copositive cone has faces which are isomorphic to positive semidefinite cones. We also look at some maximal faces of the completely positive cone and find their dimensions. Additionally we consider extreme rays of the copositive and completely positive cones and show that every extreme ray of the completely positive cone is also an exposed ray, but the copositive cone has extreme rays which are not exposed rays. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a Lipschitz optimization problem (LOP) constrained by linear functions in . In general, since it is hard to solve (LOP) directly, (LOP) is transformed into a certain problem (MP) constrained by a ball in . Despite there is no guarantee that the objective function of (MP) is quasi-convex, by using the idea of the quasi-conjugate function defined by Thach (1991) , we can construct its dual problem (DP) as a quasi-convex maximization problem. We show that the optimal value of (DP) coincides with the multiplication of the optimal value of (MP) by −1, and that each optimal solution of the primal and dual problems can be easily obtained by the other. Moreover, we formulate a bidual problem (BDP) for (MP) (that is, a dual problem for (DP)). We show that the objective function of (BDP) is a quasi-convex function majorized by the objective function of (MP) and that both optimal solution sets of (MP) and (BDP) coincide. Furthermore, we propose an outer approximation method for solving (DP). [Copyright &y& Elsevier]

Abstract: Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the past few years. However, the polynomial case has not been studied in detail due to its theoretical and computational difficulties. This paper presents an algebraic approach for solving these problems. We propose a methodology based on transforming the polynomial optimization problem to the problem of solving one or more systems of polynomial equations and we use certain Gröbner bases to solve these systems. Different transformations give different methodologies that are theoretically stated and compared by some computational tests via the algorithms that they induce. [Copyright &y& Elsevier]

Abstract: In this paper, we derive a multiplier formula for Hörmander''s parametric Marcinkiewicz integral operator. As a consequence, we prove the optimality of the kernel size condition as well as the optimality of the Block size condition. [Copyright &y& Elsevier]

Abstract: In this paper, the Lie symmetry analysis is performed on the fifth-order KdV types of equations which arise in modeling many physical phenomena. The similarity reductions and exact solutions are obtained based on the optimal system method. Then the exact analytic solutions are considered by using the power series method. [Copyright &y& Elsevier]

Abstract: This paper presents an adaptive regularization approach for solving the nonlinear model updating inverse problem. The discrimination of possible damaged elements and undamaged elements is done from results obtained in previous iterations via a new side condition which aims at (a) to limit the local change in damaged structural elements in each iteration; and (b) to force the variation of other undamaged elements close to zero. A thirty-one bar plane truss structure with multiple damages is studied. Results obtained from the proposed method are greatly improved over those obtained from the traditional Tikhonov regularization even with large noise contamination in the measurements. [Copyright &y& Elsevier]

Abstract: The partial quadratic eigenvalue assignment problem (PQEVAP) concerns reassigning a few undesired eigenvalues of a quadratic matrix pencil to suitably chosen locations and keeping the other large number of eigenvalues and eigenvectors unchanged (no spill-over). The problem naturally arises in controlling dangerous vibrations in structures by means of active feedback control design. For practical viability, the design must be robust, which requires that the norms of the feedback matrices and the condition number of the closed-loop eigenvectors are as small as possible. The problem of computing feedback matrices that satisfy the above two practical requirements is known as the Robust Partial Quadratic Eigenvalue Assignment Problem (RPQEVAP). In this paper, we formulate the RPQEVAP as an unconstrained minimization problem with the cost function involving the condition number of the closed-loop eigenvector matrix and two feedback norms. Since only a small number of eigenvalues of the open-loop quadratic pencil are computable using the state-of-the-art matrix computational techniques and/or measurable in a vibration laboratory, it is imperative that the problem is solved using these small number of eigenvalues and the corresponding eigenvectors. To this end, a class of the feedback matrices are obtained in parametric form, parameterized by a single parametric matrix, and the cost function and the required gradient formulas for the optimization problem are developed in terms of the small number of eigenvalues that are reassigned and their corresponding eigenvectors. The problem is solved directly in quadratic setting without transforming it to a standard first-order control problem and most importantly, the significant “no spill-over property” of the closed-loop eigenvalues and eigenvectors is established by means of a mathematical result. These features make the proposed method practically applicable even for very large structures. Results on numerical experiments show that the proposed method considerably reduces both feedback norms and the sensitivity of the closed-loop eigenvalues. A study on robustness of the system responses of the method under small perturbations show that the responses of the perturbed closed-loop system are compatible with perturbations. [Copyright &y& Elsevier]

Abstract: In this paper we present two different results dealing with the number of -facets of a set of points: [1.] We give structural properties of sets in the plane that achieve the optimal lower bound of -edges for a fixed ; and [2.] we show that, for , the number of -facets of a set of points in general position in is at least , and that this bound is tight in the given range of . [Copyright &y& Elsevier]

Abstract: In this paper we present a new primal-dual path-following interior-point algorithm for semidefinite optimization. The algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only full Nesterov–Todd step. Moreover, we obtain the currently best known iteration bound for the algorithm with small-update method, namely, , which is as good as the linear analogue. [Copyright &y& Elsevier]

Abstract: In this paper necessary and sufficient conditions for strict minimizers of a general vector optimization problem are given by means of different notions of graphical or epigraphical derivatives, extending some existing results in the literature. In first place, these conditions are established by means of contingent derivatives and secondly, by applying a nonconvex separation result, in terms of contingent epiderivatives and hypoderivatives. Moreover, through a variational approach, a scalarization method is developed in order to obtain scalar versions of these results. [Copyright &y& Elsevier]

Abstract: This paper adapts a technical device going back to [J. López-Gómez, Optimal uniqueness theorems and exact blow-up rates of large solutions, J. Differential Equations 224 (2006) 385–439] to ascertain the blow-up rate of the (unique) radially symmetric large solution given through the main theorem of [J. López-Gómez, Uniqueness of radially symmetric large solutions, Discrete Contin. Dyn. Syst., Supplement dedicated to the 6th AIMS Conference, Poitiers, France, 2007, pp. 677–686]. The requested underlying estimates are based upon the main theorem of [S. Cano-Casanova, J. López-Gómez, Existence, uniqueness and blow-up rate of large solutions for a canonical class of one-dimensional problems on the half-line, J. Differential Equations 244 (2008) 3180–3203]. Precisely, we show that if Ω is a ball, or an annulus, is positive and non-decreasing, satisfies , , , for every , and as , for some and , then, for each , possesses a unique positive large solution in Ω, L, which must be radially symmetric, by uniqueness, and we can estimate the exact blow-up rate of at ∂Ω in terms of p, H and f (see Theorem 1.1). [Copyright &y& Elsevier]

Abstract: The aim of this paper is to point out some sufficient constraint qualification conditions ensuring the boundedness of a set of Lagrange multipliers for vectorial optimization problems in infinite dimension. In some (smooth) cases these conditions turn out to be necessary for the existence of multipliers as well. [Copyright &y& Elsevier]

Abstract: The paper provides an upper bound on the size of a (generalized) separating hash family, a notion introduced by Stinson, Wei and Chen. The upper bound generalizes and unifies several previously known bounds which apply in special cases, namely bounds on perfect hash families, frameproof codes, secure frameproof codes and separating hash families of small type. [Copyright &y& Elsevier]

Abstract: In this paper, two conjugate dual problems based on weak efficiency to a constrained vector optimization problem are introduced. Some inclusion relations between the dual objective mappings and the properties of the Lagrangian maps and their saddle points for primal problem are discussed. Gap functions for a vector equilibrium problem are established by using the weak and strong duality. [Copyright &y& Elsevier]

Abstract: In this paper we obtain second-order optimality conditions of Karush–Kuhn–Tucker type and Fritz John one for a problem with inequality constraints and a set constraint in nonsmooth settings using second-order directional derivatives. In the necessary conditions we suppose that the objective function and the active constraints are continuously differentiable, but their gradients are not necessarily locally Lipschitz. In the sufficient conditions for a global minimum we assume that the objective function is differentiable at and second-order pseudoconvex at , a notion introduced by the authors [I. Ginchev, V.I. Ivanov, Higher-order pseudoconvex functions, in: I.V. Konnov, D.T. Luc, A.M. Rubinov (Eds.), Generalized Convexity and Related Topics, in: Lecture Notes in Econom. and Math. Systems, vol. 583, Springer, 2007, pp. 247–264], the constraints are both differentiable and quasiconvex at . In the sufficient conditions for an isolated local minimum of order two we suppose that the problem belongs to the class . We show that they do not hold for problems, which are not ones. At last a new notion parabolic local minimum is defined and it is applied to extend the sufficient conditions for an isolated local minimum from problems with data to problems with one. [Copyright &y& Elsevier]

Abstract: In this paper we analyse the behaviour, near expiry, of the free boundary appearing in the pricing of multi-dimensional American options in a financial market driven by a general multi-dimensional Ito diffusion. In particular, we prove regularity for the pricing function up to the terminal state and we establish a sufficient criteria for the conclusion that the optimal exercise boundary approaches the terminal state faster than parabolically. [Copyright &y& Elsevier]

Abstract: Many real life problems can be stated as a continuous minimax optimization problem. Well-known applications to engineering, finance, optics and other fields demonstrate the importance of having reliable methods to tackle continuous minimax problems. In this paper a new approach to the solution of continuous minimax problems over reals is introduced, using tools based on modal intervals. Continuous minimax problems, and global optimization as a particular case, are stated as the computation of semantic extensions of continuous functions, one of the key concepts of modal intervals. Modal intervals techniques allow to compute, in a guaranteed way, such semantic extensions by means of an efficient algorithm. Several examples illustrate the behavior of the algorithms in unconstrained and constrained minimax problems. [Copyright &y& Elsevier]

Abstract: The Wolfe''s duality theorems in interval-valued optimization problems are derived in this paper. Four kinds of interval-valued optimization problems are formulated. The Karush–Kuhn–Tucker optimality conditions for interval-valued optimization problems are derived for the purpose of proving the strong duality theorems. The concept of having no duality gap in weak and strong sense are also introduced, and the strong duality theorems in weak and strong sense are then derived naturally. [Copyright &y& Elsevier]

Abstract: The Kuhn–Tucker Sufficiency Theorem states that a feasible point that satisfies the Kuhn–Tucker conditions is a global minimizer for a convex programming problem for which a local minimizer is global. In this paper, we present new Kuhn–Tucker sufficiency conditions for possibly multi-extremal nonconvex mathematical programming problems which may have many local minimizers that are not global. We derive the sufficiency conditions by first constructing weighted sum of square underestimators of the objective function and then by characterizing the global optimality of the underestimators. As a consequence, we derive easily verifiable Kuhn–Tucker sufficient conditions for general quadratic programming problems with equality and inequality constraints. Numerical examples are given to illustrate the significance of our criteria for multi-extremal problems. [Copyright &y& Elsevier]

Abstract: In this paper we introduce a class of set-valued increasing-along-rays maps and present some properties of set-valued increasing-along-rays maps. We show that the increasing-along-rays property of a set-valued map is close related to the corresponding set-valued star-shaped optimization. By means of increasing-along-rays property, we investigate stability and well-posedness of set-valued star-shaped optimization. [Copyright &y& Elsevier]

Abstract: In this paper we propose a derivative-free optimization algorithm based on conditional moments for finding the maximizer of an objective function. The proposed algorithm does not require calculation or approximation of any order derivative of the objective function. The step size in iteration is determined adaptively according to the local geometrical feature of the objective function and a pre-specified quantity representing the desired precision. The theoretical properties including convergence of the method are presented. Numerical experiments comparing with the Newton, Quasi-Newton and trust region methods are given to illustrate the effectiveness of the algorithm. [Copyright &y& Elsevier]

Abstract: Any finite semifield 2-dimensional over its left nucleus and 2n-dimensional over its center defines a linear set of rank 2n of disjoint from a hyperbolic quadric and conversely [G. Lunardon, Translation ovoids, J. Geom. 76 (2003) 200–215]. Using this connection, semifields 2-dimensional over their left nucleus and 4-dimensional over their center were classified [I. Cardinali, O. Polverino, R. Trombetti, Semifield planes of order with kernel and center , European J. Combin. 27 (2006) 940–961]. In this paper we give a characterization result in the case , proving that there exist five or six non-isotopic families of such semifields, the families , ( might be empty), according to the different configurations of the associated linear sets of . Also, we prove that to any semifield belonging to the family is associated an -pseudoregulus of and we characterize the known examples of semifields of the family in terms of the associated -pseudoregulus. [Copyright &y& Elsevier]

Abstract: In this paper, the robust variance-constrained control problem is considered for uncertain stochastic systems with multiplicative noises. The norm-bounded parametric uncertainties enter into both the system and output matrices. The purpose of the problem is to design a state feedback controller such that, for all admissible parameter uncertainties, (1) the closed-loop system is exponentially mean-square quadratically stable; (2) the individual steady-state variance satisfies given upper bound constraints; and (3) the prescribed noise attenuation level is guaranteed in an sense with respect to the additive noise disturbances. A general framework is established to solve the addressed multiobjective problem by using a linear matrix inequality (LMI) approach, where the required stability, the characterization and variance constraints are all easily enforced. Within such a framework, two additional optimization problems are formulated: one is to optimize the performance, and the other is to minimize the weighted sum of the system state variances. A numerical example is provided to illustrate the effectiveness of the proposed design algorithm. [Copyright &y& Elsevier]

Abstract: The problem of the bar breakage diagnosis in electrical induction cage machines is a matter of increasing concern nowadays, due to the widely spread use of these machines in the industry. The classical approach, focused on the Fourier analysis of the steady-state current, has some drawbacks that could be avoided if a study of the transient behavior of the machine is performed. The discrete wavelet transform (DWT) is an ideal tool for this purpose, due to its suitability for the analysis of signals whose frequency spectrum is variable in time. The paper shows how the study of the high-level signals resulting from the DWT of the transient starting current of an induction motor allows the detection of a particular characteristic harmonic that occurs when a rotor bar breakage has taken place. This constitutes an alternative approach that avoids some problems that the traditional method implies and that can even lead to a wrong diagnosis of the fault. In the work, the application of the DWT for broken bar detection is optimized, regarding certain parameters of the transform such as type of the mother wavelet, number of decomposition levels, order of the mother wavelet and sampling frequency. [Copyright &y& Elsevier]

Abstract: In this paper we provide a duality theory for multiobjective optimization problems with convex objective functions and finitely many D.C. constraints. In order to do this, we study first the duality for a scalar convex optimization problem with inequality constraints defined by extended real-valued convex functions. For a family of multiobjective problems associated to the initial one we determine then, by means of the scalar duality results, their multiobjective dual problems. Finally, we consider as a special case the duality for the convex multiobjective optimization problem with convex constraints. [Copyright &y& Elsevier]

Abstract: This paper contains two results concerning linear embeddings of subsets of Euclidean space in low-dimensional normed spaces. The first is an improvement of the known dependence on in Dvoretzky''s theorem from order of to order of (except for factors). The second is a joint generalization of (Milman''s version of) Dvoretzky''s theorem and (a recent generalization by Klartag and Mendelson of) the Johnson–Lindenstrauss Lemma. [Copyright &y& Elsevier]

Abstract: Euclidean design (rotatable design) is one of the most important concepts concerning good structures consisting of finitely many points in . Optimal design is an important class of such designs studied in statistics. In this paper we consider Euclidean tight 4-designs in which are supported by a union of 2 concentric spheres centered at the origin. We prove that if is optimal on , then and is similar to a spherical tight 4-design. [Copyright &y& Elsevier]

Abstract: In this paper, we establish some relationships between vector variational-like inequality and vector optimization problems under the assumptions of α-invex functions. We identify the vector critical points, the weakly efficient points and the solutions of the weak vector variational-like inequality problems, under pseudo-α-invexity assumptions. These conditions are more general than those of existing ones in the literature. In particular, this work extends the earlier work of Ruiz-Garzon et al. [G. Ruiz-Garzon, R. Osuna-Gomez, A. Rufian-Lizan, Relationships between vector variational-like inequality and optimization problems, European J. Oper. Res. 157 (2004) 113–119] to a wider class of functions, namely the pseudo-α-invex functions studied in a recent work of Noor [M.A. Noor, On generalized preinvex functions and monotonicities, J. Inequal. Pure Appl. Math. 5 (2004) 1–9]. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a class of infinitely repeated games with imperfect public monitoring. We look at strongly symmetric perfect public equilibria with memory K: equilibria in which strategies are restricted to depend only on the last K observations of public signals. Define to be the set of payoffs of equilibria with memory K. We show that for some parameter settings, for sufficiently large K. However, for other parameter settings, we show that not only is , but that is a singleton. Moreover, this last result is essentially independent of the discount factor. [Copyright &y& Elsevier]

Abstract: In this paper by a new method we first get . Based on it, we then obtain a new asymptotic representation on the norm of the Fourier operators as follows: . [Copyright &y& Elsevier]

Abstract: In this paper, which is a continuation of [V. Timofte, On the positivity of symmetric polynomial functions. Part I: General results, J. Math. Anal. Appl. 284 (2003) 174–190] and [V. Timofte, On the positivity of symmetric polynomial functions. Part II: Lattice general results and positivity criteria for degrees 4 and 5, J. Math. Anal. Appl., in press], we study properties of extremal polynomials of degree 4, and we give the construction of some of them. The main results are Theorems 9, 13, 15, 16, and 18. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce new classes of generalized V-type I invex functions for variational problems and consider a multiobjective variational problem (VP). A number of sufficiency results are established using Lagrange multiplier conditions under various types of generalized V-type I invexity requirements. Duality results are obtained for Mond–Weir type duals under the above generalized V-type I invexity assumptions and their generalizations. [Copyright &y& Elsevier]

Abstract: In this paper the asymptotic behavior of Szász operators for locally bounded functions f is studied at points x where and exist. An asymptotic estimate of this type approximation is obtained by using some techniques and results of probability theory. The estimate essentially is the best possible for continuous points of f. [Copyright &y& Elsevier]

Abstract: In this paper, we solve a new functional equation and prove the stability of this equation. [Copyright &y& Elsevier]

Abstract: It is not a difficult task to find a weak Pareto or Pareto solution in a multiobjective linear programming (MOLP) problem. The difficulty lies in finding all these solutions and representing their structure. This paper develops an algorithm for solving this problem. We investigate the solutions and their relationships in the objective space. The algorithm determines finite number of weights, each of which corresponds to a weighted sum problems. By solving these problems, we further obtain all weak Pareto and Pareto solutions of the MOLP and their structure in the constraint space. The algorithm avoids the degeneration problem, which is a major hurdle of previous works, and presents an easy and clear solution structure. [Copyright &y& Elsevier]

Abstract: Beam stiffeners have frequently been used for raising natural frequencies of base structures. In stiffener layout optimization problems, most of the previous researches considering the position and/or the length of the stiffener as design variables dealt with structures having just simple convex shapes such as a square or rectangle. The reason was because concave shape structures have difficulties in formulating geometry constraints. In this paper, a new geometry constraint handling technique, which can define both convex and concave feasible regions and measure a degree of geometry constraint violation, was proposed. Evolution strategies (ESs) was utilized as an optimization tool. In addition, the constraint-handling technique of EVOSLINOC (EVOlution Strategies for scalar optimization with LInear and NOnlinear Constraints) was utilized to solve constrained optimization problems. From numerical examples, the proposed geometry constraint handling technique was verified and proved that the technique can easily be applied to structures in not only convex but also concave shapes, even with a protrusion or interior holes. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the set-valued vector optimization problems with constraint in locally convex spaces. We present the necessary and sufficient conditions for Henig efficient solution pair, globally proper efficient solution pair and super efficient solution pair without the ordering cones having the nonempty interior. [Copyright &y& Elsevier]

Abstract: In this paper, we extend the classes of generalized type I vector-valued functions introduced by Aghezzaf and Hachimi in [J. Global Optim. 18 (2000) 91–101] to generalized univex type I vector-valued functions and consider a multiple-objective optimization problem involving generalized type I univex functions. A number of Kuhn–Tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution. The Mond–Weir and general Mond–Weir type duality results are also presented. [Copyright &y& Elsevier]