extendable poscurv-convex – Optimization Online

Semidefinite Representation of Convex Sets

Published: 2007/06/20, Updated: 2008/07/21

Convex Optimization, Global Optimization Theory, Semi-definite Programming convex polynomials positive curvature, convex sets, extendable poscurv-convex, linear matrix inequality (lmi), modified hessian, moments, poscurv-convex, positive definite lagrange hessian (pdlh) condition, positive second fundamental form, schm"{u}dgen and putinar's matrix positivstellensatz, semialgebraic geometry, semidefinite programming, sos-concave (sos-convex), sum of squares(sos)

Let $S =\{x\in \re^n:\, g_1(x)\geq 0, \cdots, g_m(x)\geq 0\}$ be a semialgebraic set defined by multivariate polynomials $g_i(x)$. Assume $S$ is convex, compact and has nonempty interior. Let $S_i =\{x\in \re^n:\, g_i(x)\geq 0\}$, and $\bdS$ (resp. $\bdS_i$) be the boundary of $S$ (resp. $S_i$). This paper, as does the subject of semidefinite programming (SDP), concerns … Read more