Semidefinite representation of convex sets

Let be a semialgebraic set defined by multivariate polynomials g i ( x ). Assume S is convex, compact and has nonempty interior. Let , and ∂ S (resp. ∂ S i ) be the boundary of S (resp. S i ). This paper, as does the subject of semidefinite programming (SDP), concerns linear matrix inequalities (LMI...

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Bibliographic Details
Published in:	Mathematical programming Vol. 122; no. 1; pp. 21 - 64
Main Authors:	Helton, J. William, Nie, Jiawang
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer-Verlag 01.03.2010 Springer Springer Nature B.V
Subjects:	Applied mathematics Applied sciences Calculus of Variations and Optimal Control; Optimization Combinatorics Control theory Exact sciences and technology Full Length Paper Hypotheses Mathematical and Computational Physics Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Operational research and scientific management Operational research. Management science Optimization Polynomials Theorems Theoretical Poscurv-convex 65K05 Moments Convex polynomials positive curvature Schmüdgen and Putinar’s matrix Positivstellensatz Semidefinite programming (SDP) Extendable poscurv-convex Convex sets Sos-concave (sos-convex) Sum of squares(SOS) Modified Hessian 90C25 90C22 Semialgebraic geometry Positive second fundamental form Positive definite Lagrange Hessian (PDLH) condition Linear matrix inequality (LMI) 47N10 46N10 Convex set Semi definite programming Convex programming Optimization Lagrange multiplier Linear matrix inequality Mathematical programming Polynomial matrix Minimization Semi algebraic set Applied mathematics Positive definite matrix S matrix Matrix polynomial Schmüdgen and Putinar's matrix Positivstellensatz Curvature
ISSN:	0025-5610, 1436-4646
Online Access:	Get full text
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