The KKT optimality conditions for constrained programming problem with generalized convex fuzzy mappings
Authors
Abstract:
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 $alpha-$univex fuzzy mappings and get some properties. In the last, we derive necessary and sufficient Karush-Kuhn-Tucker conditions and its dual problems with generalized differentiable $alpha-$univex fuzzy mappings for fuzzy constrained programming problem.
similar resources
Equivalent Conditions of Generalized Convex Fuzzy Mappings
We obtain some equivalent conditions of (strictly) pseudoconvex and quasiconvex fuzzy mappings. These results will be useful to present some characterizations of solutions for fuzzy mathematical programming.
full textOn Sequential Optimality Conditions without Constraint Qualifications for Nonlinear Programming with Nonsmooth Convex Objective Functions
Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constrai...
full textNew optimality conditions for multiobjective fuzzy programming problems
In this paper we study fuzzy multiobjective optimization problems defined for $n$ variables. Based on a new $p$-dimensional fuzzy stationary-point definition, necessary efficiency conditions are obtained. And we prove that these conditions are also sufficient under new fuzzy generalized convexity notions. Furthermore, the results are obtained under general differentiability hypothesis.
full textOn Generalized Monotone Multifunctions with Applications to Optimality Conditions in Generalized Convex Programming
Characterization of quasiconvexity and pseudoconvexity of lower semicontinuous functions on Banach spaces are presented in terms of abstract subdifferentials relying on a Mean Value Theorem. We give some properties of the normal cone to the lower level set of f . We also obtain necessary and sufficient optimality conditions in quasiconvex and pseudoconvex programming via variational inequalities.
full textOptimality Conditions for Multiobjective Programming with Generalized (zeta, rho, theta)-Convex Set Functions
Necessary conditions for Pareto optimality in multiobjective programming with subdifferentiable set functions are established in Theorem 12 of H. C. Lai and L. J. Ž . Lin J. Math. Anal. Appl. 132, 1988, 558]571 . In this paper, we establish some sufficient conditions under which a feasible solution of such a problem will be Pareto optimal provided that a weaker convexity requirement is satisfie...
full textOptimization Tutorial 2 : Newton ’ s Method , Karush - Kuhn - Tucker ( KKT ) Conditions 3 3 Constrained Optimization and KKT Optimality Conditions
In the first part of the tutorial, we introduced the problem of unconstrained optimization, provided necessary and sufficient conditions for optimality of a solution to this problem, and described the gradient descent method for finding a (locally) optimal solution to a given unconstrained optimization problem. We now describe another method for unconstrained optimization, namely Newton’s metho...
full textMy Resources
Journal title
volume 16 issue 5
pages 77- 95
publication date 2019-10-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023