A General Framework for Convex Relaxation of Polynomial Optimization Problems over Cones
Masakazu Kojima (kojimais.titech.ac.jp)
Abstract: The class of POPs (Polynomial Optimization Problems) over cones covers a wide range of optimization problems such as $0$-$1$ integer linear and quadratic programs, nonconvex quadratic programs and bilinear matrix inequalities. This paper presents a new framework for convex relaxation of POPs over cones in terms of linear optimization problems over cones. It provides a unified treatment of many existing convex relaxation methods based on the lift-and-project linear programming procedure, the reformulation-linearization technique and the semidefinite programming relaxation for a variety of problems. It also extends the theory of convex relaxation methods, and thereby brings flexibility and richness in practical use of the theory.
Keywords: Global optimization, Convex relaxation, Nonconvex program, Quadratic program, Semidefinite program, Second-order cone program, Lift-and-project linear programming procedure, Polynomial optimization problem
Category 1: Linear, Cone and Semidefinite Programming
Category 2: Global Optimization
Citation: Journal of Operations Research Society of Japan Vol.46 (2) 125-144 (2003).
Entry Submitted: 06/09/2002
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