# Sufficient conditions for global weak Pareto solutions in multiobjective optimization

Sufficient conditions for global weak Pareto solutions in multiobjective optimization In this paper we derive new sufficient conditions for global weak Pareto solutions to set-valued optimization problems with general geometric constraints of the type \begin{aligned} \text{ maximize}\quad F(x) \quad \text{ subject} \text{ to}\quad x\in \Omega , \end{aligned} where $$F: X\rightrightarrows Z$$ is a set-valued mapping between Banach spaces with a partial order on $$Z$$ . Our main results are established by using advanced tools of variational analysis and generalized differentiation; in particular, the extremal principle and full generalized differential calculus for the subdifferential/coderivative constructions involved. Various consequences and refined versions are also considered for special classes of problems in vector optimization including those with Lipschitzian data, with convex data, with finitely many objectives, and with no constraints. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Sufficient conditions for global weak Pareto solutions in multiobjective optimization

, Volume 16 (3) – Aug 31, 2012
24 pages

/lp/springer_journal/sufficient-conditions-for-global-weak-pareto-solutions-in-L7VAsR7u99
Publisher
SP Birkhäuser Verlag Basel
Copyright © 2012 by Springer Basel AG
Subject
Mathematics; Operator Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics; Potential Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-012-0194-4
Publisher site
See Article on Publisher Site

### Abstract

In this paper we derive new sufficient conditions for global weak Pareto solutions to set-valued optimization problems with general geometric constraints of the type \begin{aligned} \text{ maximize}\quad F(x) \quad \text{ subject} \text{ to}\quad x\in \Omega , \end{aligned} where $$F: X\rightrightarrows Z$$ is a set-valued mapping between Banach spaces with a partial order on $$Z$$ . Our main results are established by using advanced tools of variational analysis and generalized differentiation; in particular, the extremal principle and full generalized differential calculus for the subdifferential/coderivative constructions involved. Various consequences and refined versions are also considered for special classes of problems in vector optimization including those with Lipschitzian data, with convex data, with finitely many objectives, and with no constraints.

### Journal

PositivitySpringer Journals

Published: Aug 31, 2012

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