Nonconvex Quadratic Programming
As we have pointed out in the preceding chapters, in deterministic global optimization it is of utmost importance to take advantage of the particular mathematical structure of the problem under study. There are in general two aspects of nonconvexity deserving special attention. First, the rank of nonconvexity, i.e. roughly speaking, the number of nonconvex variables. In Chapter 7 we have discussed decomposition methods for handling low rank nonconvex problems. The second aspect is the degree of nonconvexity, i.e. the extent to which the variables are nonconvex. This last Chapter is devoted to nonconvex optimization problems which involve only linear or quadratic functions, i.e. in a sense functions with lowest degree of nonconvexity.
KeywordsQuadratic Program Convex Envelope Nonconvex Function Nonconvex Quadratic Program Bilinear Program
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