Nonconvex Quadratic Programming via Generalized Polars.

A generalized outer polar F is constructed for nonconvex, linearly constrained, quadratic programs, which can be used in essentially the same ways as outer polars are used in integer programming. First the author discusses the derivation of valid cutting planes from F. Then the author discusses an algorithm which does not generate cuts, but uses the properties of F in a different way. Starting with a subset of the Kuhn-Tucker constraints, some of the remaining constraints are successively activated so as to construct a polytope contained in F. When this is achieved, the best among the local optima found in the process is a global optimum. Author