On Standard Quadratic Optimization Problems

A standard quadratic optimization problem (QP) consists of finding (global) maximizers of a quadratic form over the standard simplex. Standard QPs arise quite naturally in copositivity-based procedures which enable an escape from local solutions. Furthermore, several important applications yield optimization problems which can be cast into a standard QP in a straightforward way. As an example, a new continuous reformulation of the maximum weight clique problem in undirected graphs is presented which considerably improves previous attacks both as numerical stability and interpretation of the results are concerned. Apparently also for the first time, an equivalence between standard QPs and QPs on the positive orthant is established. Also, a recently presented global optimization procedure (GENF - genetical engineering via negative fitness) is shortly reviewed.