Journal
SIAM JOURNAL ON OPTIMIZATION
Volume 20, Issue 2, Pages 983-1001Publisher
SIAM PUBLICATIONS
DOI: 10.1137/080736090
Keywords
alternative theorems; quadratic inequality systems; quadratic optimization; global optimality conditions; trust-region problems
Categories
Funding
- Australian Research Council
- Korean government [ROA-2008-000-20010-0]
Ask authors/readers for more resources
We establish alternative theorems for quadratic inequality systems. Consequently, we obtain Lagrange multiplier characterizations of global optimality for classes of nonconvex quadratic optimization problems. We present a generalization of Dine's theorem to a system of two homogeneous quadratic functions with a regular cone. The class of regular cones are cones K for which (K U-K) is a subspace. As a consequence, we establish a generalization of the powerful S-lemma, which paves the way to obtain a complete characterization of global optimality for a general quadratic optimization model problem involving a system of equality constraints in addition to a single quadratic inequality constraint. We then present an alternative theorem for a system of three nonhomogeneous inequalities by way of establishing the convexity of the joint-range of three homogeneous quadratic functions using a regular cone. This yields Lagrange multiplier characterizations of global optimality for classes of trust-region type problems with two inequality constraints. Finally, we establish an alternative theorem for systems involving an arbitrary finite number of quadratic inequalities involving Z-matrices, which are matrices with nonpositive off diagonal elements, and present necessary and sufficient conditions for global optimality for classes of nonconvex inequality constrained quadratic optimization problems.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available