Globally Solving Nonconvex QPs via Completely Positive Programming∗
نویسندگان
چکیده
Nonconvex quadratic programming is an NP-hard problem that optimizes a general quadratic function over linear constraints. This paper introduces a new global optimization algorithm for this problem, which combines two ideas from the literature—finite branching based on the first-order KKT conditions and polyhedral-semidefinite relaxations of completely positive (or copositive) programs. Through a series of computational experiments comparing the new algorithm with existing codes on a diverse set of test instances, we demonstrate that the new algorithm is an attractive method for globally solving nonconvex QP.
منابع مشابه
Globally solving nonconvex quadratic programming problems via completely positive programming
Nonconvex quadratic programming (QP) is an NP-hard problem that optimizes a general quadratic function over linear constraints. This paper introduces a new global optimization algorithm for this problem, which combines two ideas from the literature—finite branching based on the first-order KKT conditions and polyhedral-semidefinite relaxations of completely positive (or copositive) programs. Th...
متن کاملAn LPCC approach to nonconvex quadratic programs
Filling a gap in nonconvex quadratic programming, this paper shows that the global resolution of a feasible quadratic program (QP), which is not known a priori to be bounded or unbounded below, can be accomplished in finite time by solving a linear program with linear complementarity constraints, i.e., an LPCC. Alternatively, this task can be divided into two LPCCs: the first confirms whether t...
متن کاملA globally convergent primal-dual active-set framework for large-scale convex quadratic optimization
We present a primal-dual active-set framework for solving large-scale convex quadratic optimization problems (QPs). In contrast to classical active-set methods, our framework allows for multiple simultaneous changes in the active-set estimate, which often leads to rapid identification of the optimal active-set regardless of the initial estimate. The iterates of our framework are the active-set ...
متن کاملD.C. Versus Copositive Bounds for Standard QP
The standard quadratic program (QPS) is minx∈∆ xT Qx, where ∆ ⊂ <n is the simplex ∆ = {x ≥ 0 | ni=1 xi = 1}. QPS can be used to formulate combinatorial problems such as the maximum stable set problem, and also arises in global optimization algorithms for general quadratic programming when the search space is partitioned using simplices. One class of “d.c.” (for “difference between convex”) boun...
متن کاملGlobally solving box-constrained nonconvex quadratic programs with semidefinite-based finite branch-and-bound
We consider a recent branch-and-bound algorithm of the authors for nonconvex quadratic programming. The algorithm is characterized by its use of semidefinite relaxations within a finite branching scheme. In this paper, we specialize the algorithm to the box-constrained case and study its implementation, which is shown to be a state-of-the-art method for globally solving box-constrained nonconve...
متن کامل