The structure of weak Pareto solution sets in piecewise linear multiobjective optimization in normed spaces |
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Authors: | XiYin Zheng XiaoQi Yang |
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Affiliation: | (1) Department of Mathematics, Yunnan University, Kunming, 650091, China;(2) Department of Applied Mathematics, the Hong Kong Polytechnic University, Hung Hum, Kowloon, Hong Kong, China |
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Abstract: | In general normed spaces,we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior.We establish that the weak Pareto optimal solution set of such a problem is the union of finitely many polyhedra and that this set is also arcwise connected under the cone convexity assumption of the objective function.Moreover,we provide necessary and suffcient conditions about the existence of weak(sharp) Pareto solutions. |
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Keywords: | piecewise linear function weak Pareto solution connectedness normed space |
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