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>The structure of weak Pareto solution sets in piecewise linear multiobjective optimization in normed spaces
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The structure of weak Pareto solution sets in piecewise linear multiobjective optimization in normed spaces
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机译:赋范空间中分段线性多目标优化中的弱帕累托解集的结构
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摘要
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 sufficient conditions about the existence of weak (sharp) Pareto solutions.
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