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Abstract: Discrete models and continuous control systems are considered in regard to optimality of their trajectories. Some aspects of the principle of optimality [1, p. 83] are analyzed, and it is shown to imply total optimality, that is, the optimality of every part of an optimal trajectory. Certain autonomous systems with free admissible variations possess this property. Nonautonomous optimal systems are not, in general, totally optimal, in which case the principle of optimality is not valid. A modification is proposed for the derivation of the main functional equation to demonstrate that dynamic programming and its functional equations are valid also in the case of nonoptimal remaining trajectories under a certain contiguity condition that is defined and analyzed in the paper. Control systems with incomplete information or structural limitations on controls do not, in general, satisfy the contiguity condition. Control problems for such systems may have optimal solutions which, however, cannot be obtained by dynamic programming. This fact is shown in an example of a widely used engineering system for which an optimal trajectory has all its remaining parts nonoptimal and noncontiguous to the optimal trajectory. The paper presents theoretical justification of dynamic programming for contiguous systems that do not conform to the principle of optimality. Examples are presented to illustrate the results which open new avenues in modeling and optimization of general (not totally optimal) control systems. [Copyright &y& Elsevier]

Abstract: In this paper we study necessary and sufficient optimality conditions for a set-valued optimization problem. Convexity of the multifunction and the domain is not required. A definition of -approximating multifunction is introduced. This multifunction is the differentiability notion applied to the problem. A characterization of weak minimizers is obtained for invex and generalized -convexlike multifunctions using the Lagrange multiplier rule. [Copyright &y& Elsevier]

Abstract: The paper deals with imperfect financial markets and provides new methods to overcome many inefficiencies caused by frictions. Transaction costs are quite general and far from linear or convex. The concepts of pseudoarbitrage and efficiency are introduced and deeply analyzed by means of both scalar and vector optimization problems. Their optimality conditions and solutions yield strategies to invest and hedging portfolios, as well as bid-ask spread improvements. They also point out the role of coalitions when dealing with these markets. Several sensitivity results will permit us to show that a significant transaction costs reduction is very often feasible in practice, as well as to measure its effect on the general efficiency of the market. All these findings may be especially important for many emerging and still illiquid spot or derivative markets (electricity markets, commodity markets, markets related to weather, inflation-linked or insurance-linked derivatives, etc.). [Copyright &y& Elsevier]

Abstract: In this paper, we consider notion of infine functions and we establish necessary and sufficient optimality conditions for a feasible solution of a multiobjective optimization problem involving mixed constraints (equality and inequality) to be an efficient or properly efficient solution. We also obtain duality theorems for Wolf type and Mond-Weir type duals under the generalized invexity assumptions. [Copyright &y& Elsevier]

Abstract: This paper studies maximality and totality of stable functions in the category of stable bifinite domains. We present three main results as follows, [o] [(1)] every maximum-preserving function is a maximal element in the stable function spaces; [(2)] a maximal stable function f : D → E is maximum-preserving if D is maximum-separable and E is completely separable; and [(3)] a stable bifinite domain D is maximum-separable if and only if for any locally distributive stable bifinite domain E, each maximal stable function f : D → E is maximum-preserving. [Copyright &y& Elsevier]

Abstract: In this paper, a kind of nonlinear optimization problems with nonlinear inequality constraints are discussed, and a new SQP feasible descent algorithm for solving the problems is presented. At each iteration of the new algorithm, a convex quadratic program (QP) which always has feasible solution is solved and a master direction is obtained, then, an improved (feasible descent) direction is yielded by updating the master direction with an explicit formula, and in order to avoid the Maratos effect, a height-order correction direction is computed by another explicit formula of the master direction and the improved direction. The new algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Furthermore, the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted. Finally, some numerical tests are reported. [Copyright &y& Elsevier]