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Do Sang Kim (dskimpknu.ac.kr) Abstract: We are interested in the existence of Pareto solutions to the vector optimization problem $$\text{\rm Min}_{\,\mathbb{R}^m_+} \{f(x) \,\, x\in \mathbb{R}^n\},$$ where $f\colon\mathbb{R}^n\to \mathbb{R}^m$ be a differentiable semialgebraic map. By using the socalled {\em tangency variety} of $f$ we first construct a semialgebraic set of dimension at most $m  1$ containing the set of Pareto values of the problem. Then we establish connections between PalaisSmale conditions, $M$tameness, and properness for the map $f$. Based on these results, we provide some sufficient conditions for the existence of Pareto solutions of the problem. We also introduce a generic class of polynomial vector optimization problems, which have at least one Pareto solution. Keywords: Existence theorems, Pareto optimal solutions, $M$tameness, PalaisSmale conditions, Properness, Semialgebraic Category 1: Other Topics (MultiCriteria Optimization ) Category 2: Nonlinear Optimization (Unconstrained Optimization ) Citation: Download: [PDF] Entry Submitted: 11/21/2016 Modify/Update this entry  
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