E. de Klerk and D.V. Pasechnik, Approximation of the stability number of a graph via copositve programming. SIAM J. Optim. 12 (2002), 875-892. Home/Search Document Details and Download
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D.C. Versus Copositive Bounds for Standard QP - Anstreicher, Burer (Correct)
....to QPS [3] Unfortunately these cones are not computationally tractable. However, it has been shown that there is a family of cones with SDP representations r , r 0, so that for any given Q, SQPS and DQPS CP are equivalent to QPS if 0 is replaced with r , for r su#ciently large [4, 9]. In [2] it is shown that the use of the cone r in place of 0 produces a lower bound v = v satisfying (2) Theorem 1 Let v DC and v CP denote the solution values in SQPS DC and SQPS CP , respectively. Then v v DC . Proof: Let X be a feasible solution in SQPS CP , and let x = ....
....matrix of a graph G, then v QPS = 1 #(G) where #(G) is the size of the maximum stable set [6] Thus a lower bound on v QPS provides an upper bound on the stability number. It is also known that for such problems 1 v CP = # # , where # # is Schrijver s strengthening of the Lovasz # number [4]. The relationship between # and # # is well known, and that between 7 v DC and v CP is described in the previous section. The relationship between # and v DC is less clear, despite the fact that there are a variety of equivalent formulations of # [5] In this section we give a formulation of # ....
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E. de Klerk and D.V. Pasechnik, Approximation of the stability number of a graph via copositve programming. SIAM J. Optim. 12 (2002), 875-892.
Any alpha(G) upper bound below chi(G) whenever alpha(G) < chi(G).. - Busygin (Correct)
....as an upper bound for the independence number and as a lower bound for the clique partition number simultaneously. Besides, there are increasingly tight sequences of polynomial time computable upper bounds for (G) based on lift and project method [3] and the concept of matrix copositivity [9]. A latin square is an n n matrix lled by integers from 1 to n so that each number occurs exactly once in any row and in any column. In the Quasigroup Completion Problem (QCP, a.k.a. latin square completion) we are given an n n array partially lled by integers from f1 : ng and it is ....
E. de Klerk and D. Pasechnik, Approximation of the stability number of a graph via copositive programming, SIAM J. Optim. 12:4 (2001) 875-892.
Improved bounds for the crossing numbers of K m,n and K n - De Klerk Maharry Self-citation (De klerk Pasechnik) (Correct)
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E. De Klerk, D.V. Pasechnik, Approximation of the stability number of a graph via copositive programming. SIAM J. Optim. 12(2002), 875--892.
On (G) (G) > 0 gap recognition and (G)-upper bounds - Stanislav Busygin Dmitrii (2003) Self-citation (Pasechnik) (Correct)
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E. de Klerk and D. Pasechnik, Approximation of the stability number of a graph via copositive programming, SIAM J. Optim. 12:4 (2001) 875-892.
On the Equivalence of Algebraic Approaches to - The Minimization Of Self-citation (De klerk) (Correct)
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E. de Klerk and D.V. Pasechnik. Approximation of the stability number of a graph via copositive programming. SIAM Journal on Optimization, 12:875-- 892, 2002.
Solving Standard Quadratic Optimization Problems Via Linear.. - Bomze, de Klerk (2001) (4 citations) Self-citation (De klerk) (Correct)
....the standard quadratic optimization problem. This is an improvement on the previous complexity result by Nesterov [10] that a 2=3 approximation is always possible) Numerical examples from various applications are provided to illustrate our approach, which extends ideas of De Klerk and Pasechnik [5] for the maximal stable set problem in a graph. Keywords: Approximation algorithms, stability number, semide nite programming, copositive cone, standard quadratic optimization 1 Introduction A standard quadratic optimization problem (standard QP) consists of nding global minimizers of a ....
....as a copositive programming problem, and subsequently approximate the copositive cone using either linear inequality systems, yielding LP relaxations; or, more re ned, systems of linear matrix inequalities (LMI s) yielding an SDP formulation. This methodology is due to De Klerk and Pasechnik [5] and Parillo [14] We will show that we obtain a polynomial time approximation for problem (1) for each 0 in this way. Such an approximation is known as a polynomial time approximation scheme (PTAS) This improves on a result by Nesterov [10] who showed that a 2=3 approximation is always ....
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E. de Klerk, D.V. Pasechnik. Approximation of the stability number of a graph via copositive programming. Manuscript, Faculty of Information Technology and Systems, Delft University of Technology, The Netherlands, 2000. (Accepted for publication in SIAM Journal of Optimization.)
Solving Standard Quadratic Optimization Problems Via Linear.. - Bomze, de Klerk (2001) (4 citations) Self-citation (De klerk) (Correct)
.... solution by approximating the cone of copositive matrices via systems of linear inequalities, and, more re ned, linear matrix inequalities (LMI s) Examples from various applications, and simulations are provided showing the validity of this approach, which extends ideas of De Klerk and Pasechnik [5] for the maximal stable set problem in a graph. Keywords: Approximation algorithms, stability number, semide nite programming, copositive cone, standard quadratic optimization 1 Introduction A standard quadratic optimization problem (standard QP) consists of nding global minimizers of a ....
....the SDP can be exponential in the size of the copositive program. In the next section we will review the approach of Parillo, and subsequently work out the implications for the copositive formulation of the general quadratic optimization problem by applying the approach of De Klerk and Pasechnik [5]. The basic idea is to replace the copositive cone in (4) by an approximation: either a polyhedral cone or a cone de ned by linear matrix inequalities. In this way we obtain a tractable approximation problem. 2 Approximations of the copositive cone Since any y 2 IR n can be written as y = x ....
[Article contains additional citation context not shown here]
E. de Klerk, D.V. Pasechnik. Approximation of the stability number of a graph via copositive programming. Manuscript, Faculty of Information Technology and Systems, Delft University of Technology, The Netherlands, 2000. (Accepted for publication in SIAM Journal of Optimization.)
D.C. versus Copositive Bounds for Standard QP - Anstreicher, Burer (2003) (Correct)
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E. de Klerk and D.V. Pasechnik, Approximation of the stability number of a graph via copositve programming. SIAM J. Optim. 12 (2002), 875-892.
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