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Multiobjective Convex Optimization in Real Banach Space
- Source :
- Symmetry, Vol 13, Iss 2148, p 2148 (2021), Symmetry, Volume 13, Issue 11
- Publication Year :
- 2021
- Publisher :
- MDPI AG, 2021.
-
Abstract
- 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.
- Subjects :
- saddle point
convex optimization
Physics and Astronomy (miscellaneous)
General Mathematics
Pareto principle
Banach space
Mathematics::Optimization and Control
Duality (optimization)
multiobjective programming
Nonlinear programming
Chemistry (miscellaneous)
Hadamard transform
Saddle point
Convex optimization
Computer Science (miscellaneous)
nonlinear programming
QA1-939
Applied mathematics
Differentiable function
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 13
- Issue :
- 2148
- Database :
- OpenAIRE
- Journal :
- Symmetry
- Accession number :
- edsair.doi.dedup.....4fbc3bca4b99e8c7535d0febbab8c364