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Structure and Weak Sharp Minimum of the Pareto Solution Set for Piecewise Linear Multiobjective Optimization

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  • X. Q. Yang

    (Hong Kong Polytechnic University)

  • N. D. Yen

    (Vietnamese Academy of Science and Technology)

Abstract

In this paper, the Pareto solution set of a piecewise linear multiobjective optimization problem in a normed space is shown to be the union of finitely many semiclosed polyhedra. If the problem is further assumed to be cone-convex, then it has the global weak sharp minimum property.

Suggested Citation

  • X. Q. Yang & N. D. Yen, 2010. "Structure and Weak Sharp Minimum of the Pareto Solution Set for Piecewise Linear Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 113-124, October.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:1:d:10.1007_s10957-010-9710-5
    DOI: 10.1007/s10957-010-9710-5
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    References listed on IDEAS

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    1. Xiaoqiang Cai & Kok-Lay Teo & Xiaoqi Yang & Xun Yu Zhou, 2000. "Portfolio Optimization Under a Minimax Rule," Management Science, INFORMS, vol. 46(7), pages 957-972, July.
    2. Y. P. Aneja & K. P. K. Nair, 1979. "Bicriteria Transportation Problem," Management Science, INFORMS, vol. 25(1), pages 73-78, January.
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    Cited by:

    1. Xi Yin Zheng & Xiaoqi Yang, 2021. "Fully Piecewise Linear Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 461-490, August.
    2. Ya Ping Fang & Nan Jing Huang & Xiao Qi Yang, 2012. "Local Smooth Representations of Parametric Semiclosed Polyhedra with Applications to Sensitivity in Piecewise Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 810-839, December.
    3. Margarita M. L. Rodríguez & José Vicente-Pérez, 2017. "On Finite Linear Systems Containing Strict Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 131-154, April.
    4. Ya Ping Fang & Kaiwen Meng & Xiao Qi Yang, 2012. "Piecewise Linear Multicriteria Programs: The Continuous Case and Its Discontinuous Generalization," Operations Research, INFORMS, vol. 60(2), pages 398-409, April.

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