Abstract In this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality conditions and, under appropriate invexity hypotheses, sufficient are proved for such nonconvex smooth vector optimization problems. Further, duals in sense Mond–Weir defined considered and several duality re...

We consider a nonsmooth semi-infinite interval-valued vector programming problem, where the objectives and constraint functions need not to be locally Lipschitz. Using Abadie’s qualification convexificators, we provide Karush–Kuhn–Tucker necessary optimality conditions by converting initial problem into bi-criteria optimization problem. Furthermore, establish sufficient under asymptotic convexi...

The aim of present paper is to study a constrained programming with generalized $alpha-$univex fuzzy mappings. In this paper we introduce the concepts of $alpha-$univex, $alpha-$preunivex, pseudo $alpha-$univex and $alpha-$unicave fuzzy mappings, and we discover that $alpha-$univex fuzzy mappings are more general than univex fuzzy mappings. Then, we discuss the relationships of generalized $alp...

We consider the generalized minimax programming problem (P) in which functions are locally Lipschitz (G, β)-invex. Not only G-sufficient but also G-necessary optimality conditions are established for problem (P). With G-necessary optimality conditions and (G, β)-invexity on hand, we construct dual problem (DI) for the primal one (P) and prove duality results between problems (P) and (DI). These...

1. A competitive equilibrium is a sequence (p * t , c * t , s * t+1) T t=0 such that (i) (c * t , s * t+1) T t=0 solves max (ct,s t+1) T t=0 T t=0 β t u(c t), subject to (1) c t + p * t s t+1 ≤ (p * t + y t)s t , ∀t c t , s t ≥ 0, ∀t s 0 = 1 and (ii) markets clear: c * t = y t , ∀t s * t = 1, ∀t 2. The equation is: p * t = β u (y t+1) u (y t) (p * t+1 + y t+1) Proof: Let (p * t , c * t , s * t+...

It is shown how one can get upper bounds for ju ? vj when u and v are the (viscosity) solutions of ut ? (Dxu))xu = 0 and vt ? (Dxv))xv = 0; respectively, in (0;1) with Dirichlet boundary conditions. Similar results are obtained for some other parabolic equations as well, including certain equations in divergence form. 1. Introduction In this paper we study the problem of how to estimate the dii...

This paper studies a class of problems consisting of minimizing a continuously differentiable function penalizedwith the so-called `0-norm over a symmetric set. These problems are hard to solve, yet prominent in many fields and applications.We first study the proximal mapping with respect to the `0-norm over symmetric sets, and provide an efficient method to attainit. The method is ...

The aim of this paper is to study first order optimality conditions for ideal efficient points in the Löwner partial order, when the data functions of the minimization problem are differentiable and convex with respect to the cone of symmetric semidefinite matrices. We develop two sets of first order necessary and sufficient conditions. The first one, formally very similar to the classical Karu...

In this note, we prove that the KKT mapping for nonlinear semidefinite optimization problem is upper Lipschitz continuous at the KKT point, under the second-order sufficient optimality conditions and the strict Robinson constraint qualification.