Abstract

We are motivated by the question of when a convex semialgebraic set in Rn\real^n is equal to the feasible set of a linear matrix inequality (LMI). Given a basic semialgebraic set, V\set{V}, which is defined by quadratic polynomials, we restrict our attention to closure of its convex hull, namely co(V)‾\closure{\chull{\set V}}. Our main result is that co(V)‾\closure{\chull{\set V}} is equal to the intersection of a finite number of LMI sets and the halfspaces supporting V\set V along a particular subset of the boundary of V\set V. As a corollary, we show that in R2\real^2, the halfspaces of concern are finite in number, so that an LMI representation for co(V)‾\closure{\chull{\set V}} always exists

Author information

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Uğur Yıldıran

Dept. of Systems Engineering, Yeditepe University, Istanbul, Turkey
and: Dept. of Electrical and Electronics Eng., Boğaziçi University, Istanbul, Turkey

uyildiran@yeditepe.edu.tr

İ. Emre Köse

Dept. of Mechanical Engineering, Boğaziçi University, Istanbul, Turkey

koseemre@boun.edu.tr

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Suggested citation

U. Yıldıran, I. E. Köse. “LMI Representations of the Convex Hulls of Quadratic Basic Semialgebraic Sets.” Journal of Convex Analysis 17 (2010), No. 2, 535–551. https://doi.org/10.68381/jca17036

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Published by Heldermann Verlag, 2010. Rights now held by Banach Press LLC.