نتایج جستجو برای quadratic optimization

تعداد نتایج: 218649  

In this paper we consider a fractional optimization problem that minimizes the ratio of two quadratic functions subject to a strictly convex quadratic constraint. First using the extension of Charnes-Cooper transformation, an equivalent homogenized quadratic reformulation of the problem is given. Then we show that under certain assumptions, it can be solved to global optimality using semidefini...

Journal: :Discrete Optimization 2014
Abraham P. Punnen, Sara Taghipour, Daniel Karapetyan, Bishnu Bhattacharyya,

We introduce the quadratic balanced optimization problem (QBOP) which can be used to model equitable distribution of resources with pairwise interaction. QBOP is strongly NP-hard even if the family of feasible solutions has a very simple structure. Several general purpose exact and heuristic algorithms are presented. Results of extensive computational experiments are reported using randomly gen...

Journal: :Optimization Methods and Software 2010
Alireza Ghaffari Hadigheh, Oleksandr Romanko, Tamás Terlaky,

In this paper we consider the Convex Quadratic Optimization problem with simultaneous perturbation in the right-hand-side of the constraints and the linear term of the objective function with different parameters. The regions with invariant optimal partitions are investigated as well as the behavior of the optimal value function on the regions. We show that identifying these regions can be done...

2007
Immanuel M. Bomze, Werner Schachinger,

A Standard Quadratic Optimization Problem (StQP) consists of maximizing a (possibly indefinite) quadratic form over the standard simplex. Likewise, in a multi-StQP we have to maximize a (possibly indefinite) quadratic form over the cartesian product of several standard simplices (of possibly different dimensions). Two converging monotone interior point methods are established. Further, we prove...

2015
Lixing Yang, Qingzhi Yang, Xiaoming Zhao, Zhenghai Huang,

Quadratically constrained quadratic programs (QQPs) problems play an important modeling role in many diverse problems. These problems are in general NP hard and numerically intractable. Semidefinite programming (SDP) relaxations often provide good approximate solutions to these hard problems. For several special cases of QQP, e.g., convex programs and trust region subproblems, SDP relaxation pr...

Journal: :SIAM Journal on Optimization 2006
Amir Beck, Yonina C. Eldar,

We consider the problem of minimizing an indefinite quadratic function subject to two quadratic inequality constraints. When the problem is defined over the complex plane we show that strong duality holds and obtain necessary and sufficient optimality conditions. We then develop a connection between the image of the real and complex spaces under a quadratic mapping, which together with the resu...

Journal: :SIAM Journal on Optimization 2007
Zhi-Quan Luo, Nikos D. Sidiropoulos, Paul Tseng, Shuzhong Zhang,

We consider the NP-hard problem of finding a minimum norm vector in n-dimensional real or complex Euclidean space, subject to m concave homogeneous quadratic constraints. We show that a semidefinite programming (SDP) relaxation for this nonconvex quadratically constrained quadratic program (QP) provides an O(m) approximation in the real case, and an O(m) approximation in the complex case. Moreo...

Journal: :SIAM Journal on Optimization 2009
Vaithilingam Jeyakumar, G. M. Lee, Guoyin Li,

We establish alternative theorems for quadratic inequality systems. Consequently, we obtain Lagrange multiplier characterizations of global optimality for classes of non-convex 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∪−K) is a subspace...

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