Abstract This paper deals with a robust multiobjective optimization problem involving nonsmooth/nonconvex real-valued functions. Under an appropriate constraint qualification, we establish necessary optimality conditions for weakly efficient solutions of the considered problem. These are presented in terms Karush-Kuhn-Tucker multipliers and convexificators related Examples illustrating our find...

In this work, we derive second-order optimality conditions for nonlinear semidefinite programming (NSDP) problems, by reformulating it as an ordinary nonlinear programming problem using squared slack variables. We first consider the correspondence between Karush-Kuhn-Tucker points and regularity conditions for the general NSDP and its reformulation via slack variables. Then, we obtain a pair of...

This paper is devoted to provide sufficient Karush Kuhn Tucker (in short, KKT) conditions of optimality second-order for a set-valued fractional minimax problem. In addition, we define duals the types Mond-Weir and Wolfe Further obtain theorems duality under contingent epi-derivative together with generalized cone convexity suppositions second-order.

In this paper, by considering the parametric technique, we study a class of fractional optimization problems involving data uncertainty in objective functional. We formulate and prove robust Karush-Kuhn-Tucker necessary optimality conditions provide their sufficiency convexity and/or concavity assumptions involved functionals. addition, to complete study, an illustrative example is presented.

This paper presents a method to verify closed-loop properties of optimizationbased controllers for deterministic and stochastic constrained polynomial discrete-time dynamical systems. The closed-loop properties amenable to the proposed technique include global and local stability, performance with respect to a given cost function (both in a deterministic and stochastic setting) and the L2 gain....

Solving numerically hydrodynamical problems of incompressible fluids arises the question of handling first order derivatives (those of pressure) in a closed container and determining its boundary conditions. A way to avoid the first point is to derive a Poisson equation for pressure, although the problem of taking the right boundary conditions still remains. To remove this problem another formu...

Introduction. In two previous notes [9],1 I stated some results which, in a general way, may be expressed as follows: If the Taylor series which represents an entire function satisfies a certain gap condition (which depends only on the order of F(z)), the zeros of F(z) —f(z) are not exceptional with respect to the proximate order of F(z) by any meromorphic function f(z) ^ w of lower order. On t...

A new parameterized binary relation is used to define minimality concepts in vector optimization. To simplify the problem of determining minimal elements the method of scalarization is applied. Necessary and sufficient conditions for the existence of minimal elements with respect to the scalarized problems are given. The multiplier rule of Lagrange is generalized. As a necessary minimality cond...

This paper deals with optimal control problems of semilinear parabolic equations with pointwise state constraints and coupled integral state-control constraints. We obtain necessary optimality conditions in the form of a Pontryagin’s minimum principle for local solutions in the sense of Lp, p ≤ +∞.