Branch-and-Cut Algorithms for the Bilinear Matrix Inequality Eigenvalue Problem
Computational Optimization and Applications
Some Fundamental Properties of Successive Convex Relaxation Methods on LCP and Related Problems
Journal of Global Optimization
Parallel Implementation of Successive Convex Relaxation Methods for Quadratic Optimization Problems
Journal of Global Optimization
An Explicit Exact SDP Relaxation for Nonlinear 0-1 Programs
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Semidefinite programming for discrete optimization and matrix completion problems
Discrete Applied Mathematics
High Performance Grid and Cluster Computing for Some Optimization Problems
SAINT-W '04 Proceedings of the 2004 Symposium on Applications and the Internet-Workshops (SAINT 2004 Workshops)
Discrete Applied Mathematics
Cuts for Conic Mixed-Integer Programming
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
A p-cone sequential relaxation procedure for 0-1 integer programs
Optimization Methods & Software - GLOBAL OPTIMIZATION
On the Slater condition for the SDP relaxations of nonconvex sets
Operations Research Letters
Lifts of Convex Sets and Cone Factorizations
Mathematics of Operations Research
A note on set-semidefinite relaxations of nonconvex quadratic programs
Journal of Global Optimization
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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 $F \subseteq C_{k+1} \subseteq C_k$ (monotonicity), (b) $\cap_{k=1}^{\infty} C_k = \text{the convex hull of F (asymptotic convergence). Our methods are extensions of the corresponding Lovász--Schrijver lift-and-project procedures with the use of SDP or LP relaxation applied to general quadratic optimization problems (QOPs) with infinitely many quadratic inequality constraints. Utilizing descriptions of sets based on cones of matrices and their duals, we establish the exact equivalence of the SDP relaxation and the semi-infinite convex QOP relaxation proposed originally by Fujie and Kojima. Using this equivalence, we investigate some fundamental features of the two methods including (a) and (b) above.