LMI Representations of the convex hulls of quadratic basic semialgebraic sets

Yildiran U., Emre Köse I.

Journal of Convex Analysis, vol.17, no.2, pp.535-551, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 2
  • Publication Date: 2010
  • Journal Name: Journal of Convex Analysis
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.535-551
  • Yıldız Technical University Affiliated: No


In this paper, we are motivated by the question of when a convex semialgebraic set in IRn is equal to the feasible set of a linear matrix inequality (LMI). Given a basic semialgebraic set, ν, which is defined by quadratic polynomials, we restrict our attention to closure of its convex hull, namely co(ν). Our main result is that co(ν) is equal to the intersection of a finite number of LMI sets and the halfspaces supporting V along a particular subset of the boundary of ν. As a corollary, we show that in IR2, the halfspaces of concern are finite in number, so that an LMI representation for co(ν) always exists. © Heldermann Verlag.