Existence of Pareto Solutions for Vector Polynomial Optimization Problems with Constraints

Yarui Duan (), Liguo Jiao (), Pengcheng Wu () and Yuying Zhou ()
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Yarui Duan: Soochow University
Liguo Jiao: Northeast Normal University
Pengcheng Wu: Soochow University
Yuying Zhou: Soochow University

Journal of Optimization Theory and Applications, 2022, vol. 195, issue 1, No 6, 148-171

Abstract: Abstract This paper deals with a vector polynomial optimization problem over a basic closed semi-algebraic set. By invoking some powerful tools from real semi-algebraic geometry, we first introduce the concept called tangency varieties; obtain the relationships of the Palais–Smale condition, Cerami condition, M-tameness, and properness related to the considered problem, in which the condition of Mangasarian–Fromovitz constraint qualification at infinity plays an essential role in deriving these relationships. At last, according to the obtained connections, we establish the existence of Pareto solutions to the problem in consideration and give some examples to illustrate our main findings.

Keywords: Vector optimization; Polynomial optimization; Pareto solutions; Palais–Smale condition; Cerami condition; Properness; 90C23; 90C29; 49J30 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02068-1

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