# Optimality Conditions for Minimizers at Infinity in Polynomial Programming

@article{Pham2017OptimalityCF, title={Optimality Conditions for Minimizers at Infinity in Polynomial Programming}, author={Tien Son Pham}, journal={Math. Oper. Res.}, year={2017}, volume={44}, pages={1381-1395} }

In this paper we study necessary optimality conditions for the optimization problem $$\textrm{infimum}f_0(x) \quad \textrm{ subject to } \quad x \in S,$$ where $f_0 \colon \mathbb{R}^n \rightarrow \mathbb{R}$ is a polynomial function and $S \subset \mathbb{R}^n$ is a set defined by polynomial inequalities. Assume that the problem is bounded below and has the Mangasarian--Fromovitz property at infinity. We first show that if the problem does {\em not} have an optimal solution, then a version at…

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