Smooth Representations of Optimal Solution Sets of Piecewise Linear Parametric Multiobjective Programs

Ya Ping Fang () and Xiao Qi Yang ()
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Ya Ping Fang: Sichuan University
Xiao Qi Yang: The Hong Kong Polytechnic University

A chapter in Variational Analysis and Generalized Differentiation in Optimization and Control, 2010, pp 163-176 from Springer

Abstract: Abstract In this chapter, we investigate the smooth representation of the (weakly) efficient solution set of a piecewise linear parametric multiobjective program. We show that if the data of a piecewise linear multiobjective program are smooth functions of a parameter then the (weakly) efficient solution set of the problem can be locally represented as a union of finitely many polyhedra whose vertices and directions are smooth functions of the parameter.

Keywords: Open Neighborhood; Vector Optimization Problem; Nondominated Solution; Smooth Representation; Weak Sharp Minimum (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-0437-9_8

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DOI: 10.1007/978-1-4419-0437-9_8

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