Nonsmooth interval-valued optimization and saddle-point optimality criteria
نویسندگان
چکیده
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 type optimality conditions are established in order to find relation between LU optimal solution of primal and saddlepoint of Lagrangian function.
منابع مشابه
Optimality conditions for Pareto efficiency and proper ideal point in set-valued nonsmooth vector optimization using contingent cone
In this paper, we first present a new important property for Bouligand tangent cone (contingent cone) of a star-shaped set. We then establish optimality conditions for Pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of Bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.
متن کاملLagrange multipliers theorem and saddle point optimality criteria in mathematical programming
We prove a version of Lagrange multipliers theorem for nonsmooth functionals defined on normed spaces. Applying these results, we extend some results about saddle point optimality criteria in mathematical programming. © 2005 Elsevier Inc. All rights reserved.
متن کاملSaddle Point and Second Order Optimality in Nondifferentiable Nonlinear Abstract Multiobjective Optimization
This article deals with a vector optimization problem with cone constraints in a Banach space setting. By making use of a real-valued Lagrangian and the concept of generalized subconvex-like functions, weakly efficient solutions are characterized through saddle point type conditions. The results, jointly with the notion of generalized Hessian (introduced in [Cominetti, R., Correa, R.: A general...
متن کاملA General Scalar-Valued Gap Function for Nonsmooth Multiobjective Semi-Infinite Programming
For a nonsmooth multiobjective mathematical programming problem governed by infinitely many constraints, we define a new gap function that generalizes the definitions of this concept in other articles. Then, we characterize the efficient, weakly efficient, and properly efficient solutions of the problem utilizing this new gap function. Our results are based on $(Phi,rho)-$invexity,...
متن کاملOn 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...
متن کامل