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

  • Ya Ping Fang
  • Xiao Qi Yang
Part of the Springer Optimization and Its Applications book series (SOIA, volume 47)


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.


Open Neighborhood Vector Optimization Problem Nondominated Solution Smooth Representation Weak Sharp Minimum 
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This work was partially supported by the Research Grants Council of Hong Kong (PolyU 5317/07E) and the National Natural Science Foundation of China (10831009 and 11001187).


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsSichuan UniversityChengduChina
  2. 2.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityKowloonHong Kong

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