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. Positivity Springer Journals

Sufficient conditions for global weak Pareto solutions in multiobjective optimization

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SP Birkhäuser Verlag Basel
Copyright © 2012 by Springer Basel AG
Mathematics; Operator Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics; Potential Theory; Fourier Analysis
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