LMI Representations of the convex hulls of quadratic basic semialgebraic sets

Yildiran U., Emre Köse I.

Journal of Convex Analysis, cilt.17, sa.2, ss.535-551, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 2
  • Basım Tarihi: 2010
  • Dergi Adı: Journal of Convex Analysis
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.535-551
  • Yıldız Teknik Üniversitesi Adresli: Hayır

Özet

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.