Non-convex quadratic programming
We wish to find all local and global optimizers for a non convex quadratic programming problem. Provided the given QP has a Hessian matrix having eigenvalues of mixed sign, we show that the local (global) optimizers of the nonconvex QP are in one to one correspondence with those of a certain multi parametric LP. We propose to solve the former problem by solving the latter. We use this and a reduction procedure to transform a given n dimensional non convex QP having in linear inequality constraints into m subproblem QP`s each one of which has n {minus} 1 variables and m linear constraints. The reduction procedure may then be applied to the subproblem QP`s. The reduction procedure terminates when either the subproblem dimensionality is reduced to 1, the subproblem is strictly concave, or the subproblem is strictly convex.
- OSTI ID:
- 35833
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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