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Dimension in Polynomial Variational Inequalities

Vu Trung Hieu(hieuvut***at***gmail.com)

Abstract: The aim of the paper is twofold. Firstly, by using the constant rank level set theorem from differential geometry, we establish sharp upper bounds for the dimensions of the solution sets of polynomial variational inequalities under mild conditions. Secondly, a classification of polynomial variational inequalities based on dimensions of their solution sets is introduced and investigated. Several illustrative examples are provided.

Keywords: polynomial variational inequality, polynomial fractional optimization, semialgebraic set, solution set, dimension

Category 1: Complementarity and Variational Inequalities


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Entry Submitted: 01/28/2020
Entry Accepted: 02/01/2020
Entry Last Modified: 01/28/2020

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