Cones of Matrices and Successive Convex Relaxations of Nonconvex Sets

Let F be a compact subset of the n-dimensional Euclidean space Rn represented by (finitely or infinitely many) quadratic inequalities. We propose two methods, one based on successive semidefinite programming (SDP) relaxations and the other on successive linear programming (LP) relaxations. Each of our methods generates a sequence of compact convex subsets Ck (k = 1, 2, . . . ) of Rn such that (a) the convex hull of F Ck+1 Ck (monotonicity), (b) k=1Ck = the convex hull of F (asymptotic convergence). Our methods are extensions of the corresponding Lov

• Type: Journal
• Year: 2000
• Where: SIAMJO
• Authors: Masakazu Kojima, Levent Tunçel
• Keywords: Convex Hull, Quadratic Optimization Problem, SIAMJO 2000, Successive Semidefinite Programming