Multiobjective Convex Optimization in Real Banach Space

In this paper, we consider convex multiobjective optimization problems with equality and inequality constraints in real Banach space. We establish saddle point necessary and sufficient Pareto optimality conditions for considered problems under some constraint qualifications. These results are motiva...

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Autores principales:	Kin Keung Lai, Mohd Hassan, Jitendra Kumar Maurya, Sanjeev Kumar Singh, Shashi Kant Mishra
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	multiobjective programming nonlinear programming convex optimization saddle point Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/b8d2ca8cb74d49d789c2df1cf311941b
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id	oai:doaj.org-article:b8d2ca8cb74d49d789c2df1cf311941b
record_format	dspace
spelling	oai:doaj.org-article:b8d2ca8cb74d49d789c2df1cf311941b2021-11-25T19:07:08ZMultiobjective Convex Optimization in Real Banach Space10.3390/sym131121482073-8994https://doaj.org/article/b8d2ca8cb74d49d789c2df1cf311941b2021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2148https://doaj.org/toc/2073-8994In this paper, we consider convex multiobjective optimization problems with equality and inequality constraints in real Banach space. We establish saddle point necessary and sufficient Pareto optimality conditions for considered problems under some constraint qualifications. These results are motivated by the symmetric results obtained in the recent article by Cobos Sánchez et al. in 2021 on Pareto optimality for multiobjective optimization problems of continuous linear operators. The discussions in this paper are also related to second order symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones due to Mishra and Wang in 2005. Further, we establish Karush–Kuhn–Tucker optimality conditions using saddle point optimality conditions for the differentiable cases and present some examples to illustrate our results. The study in this article can also be seen and extended as symmetric results of necessary and sufficient optimality conditions for vector equilibrium problems on Hadamard manifolds by Ruiz-Garzón et al. in 2019.Kin Keung LaiMohd HassanJitendra Kumar MauryaSanjeev Kumar SinghShashi Kant MishraMDPI AGarticlemultiobjective programmingnonlinear programmingconvex optimizationsaddle pointMathematicsQA1-939ENSymmetry, Vol 13, Iss 2148, p 2148 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	multiobjective programming nonlinear programming convex optimization saddle point Mathematics QA1-939
spellingShingle	multiobjective programming nonlinear programming convex optimization saddle point Mathematics QA1-939 Kin Keung Lai Mohd Hassan Jitendra Kumar Maurya Sanjeev Kumar Singh Shashi Kant Mishra Multiobjective Convex Optimization in Real Banach Space
description	In this paper, we consider convex multiobjective optimization problems with equality and inequality constraints in real Banach space. We establish saddle point necessary and sufficient Pareto optimality conditions for considered problems under some constraint qualifications. These results are motivated by the symmetric results obtained in the recent article by Cobos Sánchez et al. in 2021 on Pareto optimality for multiobjective optimization problems of continuous linear operators. The discussions in this paper are also related to second order symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones due to Mishra and Wang in 2005. Further, we establish Karush–Kuhn–Tucker optimality conditions using saddle point optimality conditions for the differentiable cases and present some examples to illustrate our results. The study in this article can also be seen and extended as symmetric results of necessary and sufficient optimality conditions for vector equilibrium problems on Hadamard manifolds by Ruiz-Garzón et al. in 2019.
format	article
author	Kin Keung Lai Mohd Hassan Jitendra Kumar Maurya Sanjeev Kumar Singh Shashi Kant Mishra
author_facet	Kin Keung Lai Mohd Hassan Jitendra Kumar Maurya Sanjeev Kumar Singh Shashi Kant Mishra
author_sort	Kin Keung Lai
title	Multiobjective Convex Optimization in Real Banach Space
title_short	Multiobjective Convex Optimization in Real Banach Space
title_full	Multiobjective Convex Optimization in Real Banach Space
title_fullStr	Multiobjective Convex Optimization in Real Banach Space
title_full_unstemmed	Multiobjective Convex Optimization in Real Banach Space
title_sort	multiobjective convex optimization in real banach space
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/b8d2ca8cb74d49d789c2df1cf311941b
work_keys_str_mv	AT kinkeunglai multiobjectiveconvexoptimizationinrealbanachspace AT mohdhassan multiobjectiveconvexoptimizationinrealbanachspace AT jitendrakumarmaurya multiobjectiveconvexoptimizationinrealbanachspace AT sanjeevkumarsingh multiobjectiveconvexoptimizationinrealbanachspace AT shashikantmishra multiobjectiveconvexoptimizationinrealbanachspace
_version_	1718410301351657472

Multiobjective Convex Optimization in Real Banach Space

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