S. Burer and R.D.C. Monteiro. A General Framework for Establishing Polynomial Convergence of Long-Step Methods for Semide nite Programming. Working paper, School of ISyE, Georgia Tech, USA, August 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... Jansen et al. 19] For a complete treatment see also [36] Considerable interest has arisen recently in generalizing weighted centers to semidefinite programming, and several competing approaches have been developed by Monteiro Pang [31] Sturm Zhang [39] Monteiro Zanjacomo [29] Burer Monteiro [3] and Burer Monteiro Zhang [4, 5] In this section we present a generalization of 155 weighted centers to the more general framework of self scaled conic programming. Lemma 4.3.1. Let (X; S) be a congruent square root field for the self scaled barrier functional F 2 C 3 (K ffi ; R) Suppose ....

....fashion, and for every k 2 N let T k ae T be the subset consisting of the elements of T of order k, i.e. containing k nodes. For 2 T let H denote the unique element of E such that H . Each 2 T can be written in a unique fashion in the form [1] Gamma Gamma [2] Gamma Gamma [3] . Gamma Gamma [l] Gamma Gamma ffl ffl ffl ffl ffl ffl ffl ffl ffl for some [1] l] 2 T of order strictly less than k and where l 2 N 0 . Let this relationship between and [1] l] 2 T be captured notationally by writing = R Gamma [1] ....

S. Burer and R.D.C. Monteiro. A General Framework for Establishing Polynomial Convergence of Long-Step Methods for Semidefinite Programming. School of Industrial and Systems Engineering, Georgia Institute of Technology Atlanta, GA 30332, August 1999.

....developed by Kojima Mizuno Yoshise [10] Monteiro Adler [16] Mizuno [12] Jansen Roos Terlaky Vial [7, 8] Todd [25] and others. Various generalization of V space have been developed in the context of semidefinite programming by Sturm Zhang [23, 24] Monteiro Zanjacomo [15] and Burer Monteiro [1], in the more general context of self scaled conic programming by Tuncel [28] and a related technique has been developed by Tuncel [29] for general convex conic programming problems. The notion of square root fields we present in this article is most closely related to Tuncel s work [28] and can ....

S. Burer and R.D.C. Monteiro. A General Framework for Establishing Polynomial Convergence of Long-Step Methods for Semidefinite Programming. Working paper, School of ISyE, Georgia Tech, USA, August 1999.

.... methods for linear programming (see e.g. Kojima Mizuno Yoshise [12] Monteiro Adler [18] Mizuno [14] Jansen Roos Terlaky Vial [9, 10] Todd [27] Related generalizations to semidefinite programming have been analyzed by Sturm Zhang [25, 26] Monteiro Zanjacomo [17] and Burer Monteiro [1]. Primal dual interior point methods for convex optimization problems are designed to solve a problem and its dual jointly by making use of convex duality theory. The paradigm for such algorithms usually is to reduce the duality gap between primal and dual approximate solutions to zero. In the V ....

S. Burer and R.D.C. Monteiro. A General Framework for Establishing Polynomial Convergence of Long-Step Methods for Semidefinite Programming. Working paper, School of ISyE, Georgia Tech, USA, August 1999.

.... [18] Monteiro Adler [25] Mizuno [21] JansenRoos Terlaky Vial [15, 16] For various generalizations of some aspects of this theory and for other related material see also Monteiro Pang [26] Sturm Zhang [33] MonteiroZanjacomo [24] Tuncel [37, 38] Todd [34] and Burer Monteiro [1]. target directions are thus a promising family of search directions for use in a unifying theory of primal dual interior point methods for a large class of convex optimization problems including linear, semidefinite and second order cone programming. Target directions are a rather flexible tool ....

....2 E , 2. if p; q 2 E then t 7 Theta p; R t 0 q( d 2 E . E can be indexed by a set of oriented rooted trees by recursive application of the following rules: 1. t 7 a(t) is associated with the tree consisting of a single node. a 0 : ffl 2. If p; q 2 E are associated with the trees [1] and [2] respectively, then the function t 7 Theta p; R t 0 q( d 2 E is associated with the tree obtained by appending a new root to [2] and joining the resulting tree with [1] via a new root on the left: p [1] q [2] h p( Delta) Z Delta 0 q( d i [1] ....

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S. Burer and R.D.C. Monteiro. A General Framework for Establishing Polynomial Convergence of Long-Step Methods for Semidefinite Programming. Working paper, School of ISyE, Georgia Tech, USA, August 1999.

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S. Burer and R.D.C. Monteiro. A General Framework for Establishing Polynomial Convergence of Long-Step Methods for Semide nite Programming. Working paper, School of ISyE, Georgia Tech, USA, August 1999.

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S. BURER and R.D.C. MONTEIRO. A general framework for establishing polynomial convergence of long-step methods for semidefinite programming. Technical report, Georgia Tech, Atlanta, GA, 1999. accepted Optimization Methods and Software.

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