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Strong Karush–Kuhn–Tucker Optimality Conditions for Borwein Properly Efficient Solutions of Multiobjective Semi-infinite Programming

Strong Karush–Kuhn–Tucker Optimality Conditions for Borwein Properly Efficient Solutions of... In this paper, we study strong Karush–Kuhn–Tucker optimality conditions for Borwein properly efficient solutions of multiobjective semi-infinite programming. By using some regularity conditions in the sense of Mordukhovich subdifferentials and Clarke subdifferentials, we obtain some strong necessary optimality conditions for Borwein properly efficient solutions. Some examples are also provided to illustrate that our regularity conditions have more advantages than the previous regularity conditions in some cases. Keywords Multiobjective semi-infinite programming · Mordukhovich subdifferentials · Clarke subdifferentials · Borwein properly efficient solutions · Strong KKT optimality conditions Mathematics Subject Classification 90C46 · 90C29 · 90C34 · 49J52 1 Introduction The multiobjective optimization problem (MOP) with an infinite number of constraints is called multiobjective semi-infinite programming (MSIP). Due to the nature of con- flict over the objectives, it is hard to find an ideal solution that optimizes all the objectives simultaneously. Hence, Pareto efficient solutions and many types of proper efficient solutions were introduced, see e.g. the books (Ehrgott 2005;Luc 1989), the review (Guerragio et al. 1994), the recent paper (Ha 2011) and references therein. To find the efficient solutions, weak and strong Karush–Kuhn–Tucker (KKT) optimality conditions were studied. Strong KKT optimality conditions give more information Le Thanh Tung lttung@ctu.edu.vn Department http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

Strong Karush–Kuhn–Tucker Optimality Conditions for Borwein Properly Efficient Solutions of Multiobjective Semi-infinite Programming

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References (36)

Publisher
Springer Journals
Copyright
Copyright © 2019 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-019-00190-9
Publisher site
See Article on Publisher Site

Abstract

In this paper, we study strong Karush–Kuhn–Tucker optimality conditions for Borwein properly efficient solutions of multiobjective semi-infinite programming. By using some regularity conditions in the sense of Mordukhovich subdifferentials and Clarke subdifferentials, we obtain some strong necessary optimality conditions for Borwein properly efficient solutions. Some examples are also provided to illustrate that our regularity conditions have more advantages than the previous regularity conditions in some cases. Keywords Multiobjective semi-infinite programming · Mordukhovich subdifferentials · Clarke subdifferentials · Borwein properly efficient solutions · Strong KKT optimality conditions Mathematics Subject Classification 90C46 · 90C29 · 90C34 · 49J52 1 Introduction The multiobjective optimization problem (MOP) with an infinite number of constraints is called multiobjective semi-infinite programming (MSIP). Due to the nature of con- flict over the objectives, it is hard to find an ideal solution that optimizes all the objectives simultaneously. Hence, Pareto efficient solutions and many types of proper efficient solutions were introduced, see e.g. the books (Ehrgott 2005;Luc 1989), the review (Guerragio et al. 1994), the recent paper (Ha 2011) and references therein. To find the efficient solutions, weak and strong Karush–Kuhn–Tucker (KKT) optimality conditions were studied. Strong KKT optimality conditions give more information Le Thanh Tung lttung@ctu.edu.vn Department

Journal

Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals

Published: Dec 13, 2019

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