Copositive Programming by Simplicial Partition
نویسنده
چکیده
Copositivity plays an important role in combinatorial and quadratic optimization since setting up a linear optimization problem over the copositive cone leads to exact reformulations of combinatorial and quadratic programming problems. A copositive programming problem may be approached checking copositivity of several matrices built with different values of the variable and the solution is the extreme value for which the matrix is copositive. However, this approach has some shortcomings. In this paper, we develop a simplicial partition algorithm for copositive programming to overcome the shortcomings. The algorithm has been investigated experimentally on a number of problems.
منابع مشابه
Finding the Number of Members with Certain Relationships in Social Networks and Big Size Organizations using Copositive Programming
In social networks and big size organizations, finding the number of members that all of them have a certain relationship w* is an important problem for managers, as well the number of members that none of them has not the relationship (w*). Considering the members as vertices and the relationship as edges, w* and w* denote the clique number and the number of edges in the independent graph, re...
متن کاملApproximation of Copositive Programming via Linear Programming Using Second Order Sum of Square Decomposition
In this paper, we improve the previously known result of approximating the cone of copositive matrices. We approximate the cone of copos-itive matrices by a set of linear matrices inequalities using the second order sum of square decomposition. Hence, a copositive programming can be approximated more accurately by a linear programming.
متن کاملCopositive Programming – a Survey
Copositive programming is a relatively young field in mathematical optimization. It can be seen as a generalization of semidefinite programming, since it means optimizing over the cone of so called copositive matrices. Like semidefinite programming, it has proved particularly useful in combinatorial and quadratic optimization. The purpose of this survey is to introduce the field to interested r...
متن کاملAn algorithm for determining copositive matrices
In this paper, we present an algorithm of simple exponential growth called COPOMATRIX for determining the copositivity of a real symmetric matrix. The core of this algorithm is a decomposition theorem, which is used to deal with simplicial subdivision of T̂ = {y ∈ ∆m|β y ≤ 0} on the standard simplex ∆m, where each component of the vector β is -1, 0 or 1.
متن کاملIndefinite copositive matrices with exactly one positive eigenvalue or exactly one negative eigenvalue
Checking copositivity of a matrix is a co-NP-complete problem. This paper studies copositive matrices with certain spectral properties. It shows that an indefinite matrix with exactly one positive eigenvalue is copositive if and only if the matrix is nonnegative. Moreover, it shows that finding out if a matrix with exactly one negative eigenvalue is strictly copositive or not can be formulated ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Informatica, Lith. Acad. Sci.
دوره 22 شماره
صفحات -
تاریخ انتشار 2011