The vector criterion and set criterion are two defining approaches of solutions for the set-valued optimization problems. In this paper, the optimality conditions of both criteria of solutions are established for the set-valued optimization problems. By using Studniarski derivatives, the necessary and sufficient optimality conditions are derived in the sense of vector and set optimization.

We have recently shown that the widely known LMS algorithm is an H 1 optimal estimator. The H 1 criterion has been introduced, initially in the control theory literature, as a means to ensure robust performance in the face of model uncertainties and lack of statistical information on the exogenous signals. We extend here our analysis to the nonlinear setting often encountered in neural networks...

Topology optimization is often used in the conceptual design stage as a preprocessing tool to obtain overall material distribution in the solution domain. The resulting topology is then used as an initial guess for shape optimization. It is always desirable to use fine computational grid to obtain high-resolution layouts that minimize the need for shape optimization and post processing [1], but...

A B S T RAe T This paper considers the problem of minimizing a convex-differentiable function subject to convex differentiable constraints. Necessary and sufficient conditions (not requiring any constraints qualification) for a point to be an optimal solution are given in terms of a parametric I inear program. Dual characterization theorems are then derived, which generalizes the classical resu...

Among the major difficulties that one may encounter when estimating parameters in a nonlinear regression model are the non-uniqueness of the estimator, its instability with respect to small perturbations of the observations and the presence of local optimizers of the estimation criterion. We show that these estimability issues can be taken into account at the design stage, through the definitio...

Dynamic synthesis of human movements raises the question of the selection of a suitable performance criterion able to generate proper dynamic behaviors. Two quite different criteria are likely to be appropriate candidates: the minimum effort cost (or sthenic criterion) and the minimum energy cost. The paper is aimed at clarifying the dynamic effects of these two fundamental criteria when consid...

We consider the system of articulators “jaw – tip of the tongue” in order to investigate instant and integral optimality criteria in the variational approach to the solution of speech inverse problem “from total displacement of articulators to their controls”. The required experimental data i.e., coordinates of the tip of the tongue and lower incisor have been measured by the use of the X-ray m...

In this article, we focus our attention on a nonsmooth interval-valued optimization problem and establish sufficient optimality conditions for a feasible solution to be a LU optimal solution under the invexity assumption. Appropriate duality theorems for Wolfe and Mond-Weir type duals are presented in order to relate the LU optimal solution of primal and dual programs. Moreover, saddle-point ty...

Automatic segmentation of the ECG is important in both clinical and research settings. Past algorithms have relied on incorporation of detailed heuristics. In this paper we avoid heuristics by employing a best-basis algorithm. As large variability of the local SNR causes the standard en-tropy criterion to produce an overly-ne segmentation, we introduce a novel optimality criterion which is base...

This paper presents a canonical duality theory for solving nonconvex polynomial programming problems subjected to box constraints. It is proved that under certain conditions, the constrained nonconvex problems can be converted to the so-called canonical (perfect) dual problems, which can be solved by deterministic methods. Both global and local extrema of the primal problems can be identified b...