scholarly journals Approximate optimality for quasi approximate solutions in nonsmooth semi-infinite programming problems, using ε-upper semi-regular semi-convexificators

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 2073-2089
Author(s):  
Jutamas Kerdkaew ◽  
Rabian Wangkeeree ◽  
Gue Lee
Keyword(s):  
Optimality Conditions ◽  
Efficient Solution ◽  
Approximate Solutions ◽  
Sufficient Optimality Conditions ◽  
Quasiconvex Functions ◽  
Weakly Efficient Solution ◽  
Multi Objective ◽  
New Concepts ◽  
Pseudoconvex Functions ◽  
Infinite Programming

In this paper, we study optimality conditions of quasi approximate solutions for nonsmooth semi-infinite programming problems (for short, (SIP)), in terms of ?-upper semi-regular semi-convexificator which is introduced here. Some classes of functions, namely (?-?*?)-pseudoconvex functions and (?-?*?)-quasiconvex functions with respect to a given ?-upper semi-regular semi-convexificator are introduced, respectively. By utilizing these new concepts, sufficient optimality conditions of approximate solutions for the nonsmooth (SIP) are established. Moreover, as an application, optimality conditions of quasi approximate weakly efficient solution for nonsmooth multi-objective semi-infinite programming problems (for short, (MOSIP)) are presented.

scholarly journals Optimality conditions and duality for multiobjective semi-infinite programming with data uncertainty via Mordukhovich subdifferential

2021 ◽  
pp. 13-13
Author(s):  
Thanh-Hung Pham
Keyword(s):  
Optimality Conditions ◽  
Optimization Problems ◽  
Data Uncertainty ◽  
Mordukhovich Subdifferential ◽  
New Concepts ◽  
Infinite Programming

Based on the notation of Mordukhovich subdifferential in [27], we propose some of new concepts of convexity to establish optimality conditions for quasi ?-solutions for nonlinear semi-infinite optimization problems with data uncertainty in constraints. Moreover, some examples are given to illustrate the obtained results.

scholarly journals Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming

2020 ◽  
Author(s):  
Mohsine Jennane ◽  
El Mostafa Kalmoun ◽  
Lahoussine Lafhim
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualification ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Convexity Assumption ◽  
Locally Lipschitz ◽  
Infinite Programming ◽  
Asymptotic Convexity ◽  
Interval Valued

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

On nondifferentiable minimax semi-infinite programming problems in complex spaces

2016 ◽  
Vol 23 (3) ◽  
pp. 367-380
Author(s):  
Anurag Jayswal ◽  
Krishna Kummari
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Complex Space ◽  
Sufficient Optimality Conditions ◽  
Dual Problems ◽  
Complex Spaces ◽  
Infinite Programming ◽  
Primal And Dual Problems ◽  
Primal And Dual ◽  
Necessary And Sufficient

AbstractThe purpose of this paper is to study a nondifferentiable minimax semi-infinite programming problem in a complex space. For such a semi-infinite programming problem, necessary and sufficient optimality conditions are established by utilizing the invexity assumptions. Subsequently, these optimality conditions are utilized as a basis for formulating dual problems. In order to relate the primal and dual problems, we have also derived appropriate duality theorems.

Sign in / Sign up

Export Citation Format

Share Document