ABSTRACT
This chapter discusses the nonconvex quadratic programming problems. It analyses that the optimality conditions are necessary for a strong local minimum and formulate conditions which are sufficient for a strong local minimum. The chapter formulates a variation of Algorithm 4 which will determine a strong local minimum for a nonconvex quadratic program. Algorithm 4, by itself, will determine a point which satisfies the necessary conditions for a strong local minimum. When such a point is reached, tests are introduced to see if this point is a strong local minimum. If it is, the algorithm terminates. A major difference between convex and nonconvex quadratic programming problems is that for the former any local minimizer is also a global minimizer whereas the latter may have many local minimizers. Algorithms that are designed for the nonconvex case will in general find only a strong local minimum, with no guarantee that is a global minimizer.
