scholarly journals Optimality Conditions for Nonsmooth Generalized Semi-Infinite Programs

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Zhangyou Chen ◽  
Zhe Chen
Keyword(s):  
Optimality Conditions ◽  
Parametric Optimization ◽  
Necessary Optimality Conditions ◽  
Generalized Differentiation ◽  
Value Functions ◽  
Infinite Programming

We consider a class of nonsmooth generalized semi-infinite programming problems. We apply results from parametric optimization to the lower level problems of generalized semi-infinite programming problems to get estimates for the value functions of the lower level problems and thus derive necessary optimality conditions for generalized semi-infinite programming problems. We also derive some new estimates for the value functions of the lower level problems in terms of generalized differentiation and further obtain the necessary optimality conditions.

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.

NECESSARY OPTIMALITY CONDITIONS FOR SUPER MINIMIZERS IN STRUCTURAL PROBLEMS OF MULTIOBJECTIVE OPTIMIZATION

2009 ◽  
Vol 02 (02) ◽  
pp. 321-358 ◽  
Author(s):  
Lu-Chuan Zeng
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Variational Analysis ◽  
Necessary Conditions ◽  
Necessary Optimality Conditions ◽  
Generalized Differentiation ◽  
Infinite Dimensional ◽  
Structural Problems ◽  
Constrained Problems ◽  
Finite Dimensional

The primary goal of this paper is to study the so-called super minimizers of the sum F1 + F2 related to the concept of super efficiency in constrained problems of multiobjective optimization, where each cost mapping Fi is generally set-valued for i = 1, 2. We will derive necessary conditions (of the subdifferential type) for super minimizers of the sum F1 + F2 on the basis of advanced tools of variational analysis and generalized differentiation that are new in both finite-dimensional and infinite-dimensional settings for problems with single-valued and set-valued objectives.

scholarly journals Variational Analysis in Semi-Infinite and Infinite Programming, II: Necessary Optimality Conditions

2010 ◽  
Vol 20 (6) ◽  
pp. 2788-2806 ◽  
Author(s):  
M. J. Cánovas ◽  
M. A. López ◽  
B. S. Mordukhovich ◽  
J. Parra
Keyword(s):  
Optimality Conditions ◽  
Variational Analysis ◽  
Necessary Optimality Conditions ◽  
Infinite Programming

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

2021 ◽  
Author(s):  
Nazih Abderrazzak Gadhi ◽  
Aissam Ichatouhane
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Necessary Optimality Conditions ◽  
Infinite Interval ◽  
Critical Response ◽  
Infinite Programming ◽  
Interval Valued

Necessary optimality conditions for a nonsmooth semi-infinite interval-valued vector programming problem are given in the paper by Jennane et all. (RAIRO-Oper. Res. doi: 10.1051/ro/2020066,2020). Having noticed inconsistencies in their paper, Gadhi and Ichatouhane (RAIRO-Oper. Res. doi:10.1051/ro/2020107, 2020) made the necessary corrections and proposed what they considered a more pertinent formulation of their main Theorem. Recently, Jennane et all. (RAIRO-Oper. Res. doi: 10.1051/ro/2020134) have criticised our work. This note is a critical response to this criticism.

Strong Karush–Kuhn–Tucker optimality conditions for multiobjective semi-infinite programming via tangential subdifferential

2018 ◽  
Vol 52 (4-5) ◽  
pp. 1019-1041 ◽  
Author(s):  
Le Thanh Tung
Keyword(s):  
Optimality Conditions ◽  
Necessary Optimality Conditions ◽  
Efficient Solutions ◽  
Regularity Conditions ◽  
Infinite Programming ◽  
Kkt Optimality Conditions ◽  
Theoretical Results

The main aim of this paper is to study strong Karush–Kuhn–Tucker (KKT) optimality conditions for nonsmooth multiobjective semi-infinite programming (MSIP) problems. By using tangential subdifferential and suitable regularity conditions, we establish some strong necessary optimality conditions for some types of efficient solutions of nonsmooth MSIP problems. In addition to the theoretical results, some examples are provided to illustrate the advantages of our outcomes.

scholarly journals Distance estimates for state constrained trajectories of infinite dimensional differential inclusions

2018 ◽  
Vol 24 (3) ◽  
pp. 1207-1229 ◽  
Author(s):  
Helene Frankowska ◽  
Elsa M. Marchini ◽  
Marco Mazzola
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Lipschitz Continuity ◽  
Necessary Optimality Conditions ◽  
Variational Inclusions ◽  
Value Functions ◽  
Infinite Dimensional

This paper concerns estimates on the distance between a trajectory of a differential inclusion and the set of feasible trajectories of the same inclusion, feasible meaning confined to a given set of constraints. We apply these estimates to investigate Lipschitz continuity of the value functions arising in optimal control, and to variational inclusions, useful for proving non degenerate necessary optimality conditions. The main feature of our analysis is the infinite dimensional framework, which can be applied to models involving PDEs.

Sign in / Sign up

Export Citation Format

Share Document