0-1 Optimization of Quadratic Form by Expanding the Parameter Space

Abstract

This paper is concerned with the boolean quadratic optimization problem. We formulate and analyze a class of non-convex relaxation problems which includes the relaxation problem with complex variables and the SDP relaxation problem as special cases. The effects of expanding the parameter space of decision variables to a space of hypercomplex number are investigated. It is shown that for any instance of problem data the relaxation problem in complex variable is the strongest non-convex relaxation among the relaxations (in our formulation) under the condition of having “monotonically decreasing path” which connects any two feasible solutions of the original problem.