M. Kojima, S. Shindoh, and S. Hara. Interior{point methods for the monotone linear complementarity problem in symmetric matrices. SIAM J. Optim., 7(1):86-125, Feb. 1997. Home/Search Document Not in Database Summary Related Articles Check |
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Semidefinite Programming - Helmberg (1999) (Correct)
....Germany. helmberg zib.de, http: www.zib.de helmberg 1 main attractions of semide nite programming. We present a small selection in Section 6. In Section 7, we sketch the algorithms which, in our opinion, dominate in current implementational e orts, namely, primal dual interior point algorithms [19, 26, 32, 1], a potential reduction algorithm[5] and the spectral bundle method[18] We also provide some guidelines on what classes of problems they might best be employed. We conclude by giving a short outlook in Section 8. 2 The Cone of Positive Semide nite Matrices We rst review some basic notions form ....
....but (in general) an unsymmetric X . Since the next iterate X X has to be a symmetric positive de nite matrix this is a serious problem. A number of approaches have been proposed to get around this diculty. We present only three (see [42] for a survey on search directions) The rst approach [19, 26] allows X to be unsymmetric in order to guarantee that the system is solvable. The skew symmetric part of X is then ignored and the symmetric part constitutes the new step direction, XZ X Z = I XZ; X = X X T 2 : 15) The second approach is based on the concept of self scaled ....
M. Kojima, S. Shindoh, and S. Hara. Interior{point methods for the monotone linear complementarity problem in symmetric matrices. SIAM J. Optim., 7(1):86-125, Feb. 1997.
A Spectral Bundle Method with Bounds - Helmberg, Kiwiel (1999) (8 citations) (Correct)
....A I X = b I ; A I X b I ; X 0; D) min hb; yi ; s.t. Z = A T y C; Z 0; y I 0; where the cost matrix C 2 S n and the right hand side vector b 2 IR m are given. In most applications, A i are (sparse) matrices of rank one or two and C is sparse. Primal dual interior point methods [1, 11, 14, 17], which are most commonly used for solving problem (P) o er few opportunities to exploit its structure. Their work per iteration is typically dominated by the factorization of a dense symmetric positive de nite matrix of order m, and by one or more factorizations of the variable X during the line ....
M. Kojima, S. Shindoh, and S. Hara. Interior{point methods for the monotone linear complementarity problem in symmetric matrices. SIAM J. Optim., 7(1):86-125, Feb. 1997. 17
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