期刊
SIAM JOURNAL ON OPTIMIZATION
卷 20, 期 2, 页码 983-1001出版社
SIAM PUBLICATIONS
DOI: 10.1137/080736090
关键词
alternative theorems; quadratic inequality systems; quadratic optimization; global optimality conditions; trust-region problems
资金
- Australian Research Council
- Korean government [ROA-2008-000-20010-0]
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.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据