R.D.C. MONTEIRO and T. TSUCHIYA. Polynomiality of primal-dual algorithms for semidefinite linear complementarity problems based on the Kojima-Shindoh-Hara family of directions. Math. Programming, 84:39--53, 1999. Home/Search Document Details and Download
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Nonsymmetric Search Directions for Semidefinite Programming - Sheng, Potra (1997) (4 citations) (Correct)
....Haeberly, and Overton [1] considered instead of (1.4) the symmetric equation XZ ZX = 2I: 1.5) Zhang [11] proposed a generalized symmetrization of the form 1 2 [P Gamma1 XZP (P Gamma1 XZP ) T ] I; 1.6) where P can be any nonsingular matrix. Recently, Monteiro and Tsuchiya [5] considered the symmetric central path equations Z 1=2 XZ 1=2 = I; X 1=2 ZX 1=2 = I: 1.7) Linearization of the above symmetric central path equations leads to different search directions. The most commonly used directions are the XZ ZX or AHO direction [1] the HKM direction [2, 3, 4] ....
R. D. C. Monteiro and T. Tsuchiya. Polynomiality of primal-dual algorithms for semidefinite linear complementarity problems based on the Kojima-Shindoh-Hara family of directions. Technical report, The Institute of Statistical Mathematics, Tokyo, August 1996.
A General Framework for Establishing Polynomial Convergence.. - Burer, Monteiro (1999) (6 citations) Self-citation (Monteiro) (Correct)
....time. In the past several years, a major part of the research into SDP has focused on both the theoretical and practical solution of SDP problems using extensions of interior point methods for LP. Many authors have proposed interior point algorithms for solving SDP problems (see for example [1, 2, 4, 6, 7, 8, 9, 10, 11, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26]) Many of the recent works on interior point algorithms for SDP are concentrated on primal dual methods. Feasible primal dual path following algorithms for SDP simultaneously solve the primal and dual SDP problems by maintaining primal feasibility in X and dual feasibility in (S; y) while ....
....however, results in an equation of the form X DeltaS DeltaX S = I Gamma XS; 1) which in general yields nonsymmetric directions. Many authors have investigated alternate yet equivalent equations of the central path for which Newton s method does yield symmetric directions (see for example [2, 4, 7, 10, 11, 13, 14, 17, 20, 24]) The work of these authors was based on research supported by the National Science Foundation under grants INT 9600343, CCR 9700448 and CCR 9902010. y School of Mathematics, Georgia Tech, Atlanta, Georgia 30332, USA. email: burer math.gatech.edu) z School of ISyE, Georgia Tech, Atlanta, ....
R. D. C. Monteiro and T. Tsuchiya. Polynomiality of primal-dual algorithms for semidefinite linear complementarity problems based on the Kojima-Shindoh-Hara family of directions. Mathematical Programming, 84:39--53, 1999.
Implementation Of Primal-Dual Methods For Semidefinite.. - Monteiro.. (1997) (10 citations) Self-citation (Monteiro) (Correct)
.... programming, interior point methods, path following methods, predictor corrector methods, higher order methods, Newton directions, central path, numerical implementation 1 Introduction Many authors have proposed interior point algorithms for solving semidefinite programming (SDP) problems (see [1, 2, 5, 9, 12, 14, 15, 16, 17, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34]) Most of these more recent works are concentrated on primal dual methods. One of the main goals of this paper is the implementation of primal dual path following and predictor corrector algorithms based on two pure This work was partly supported by the NSF grants CCR 9700448, CCR 9902010 and ....
R. D. C. Monteiro and T. Tsuchiya. Polynomiality of primal-dual algorithms for semidefinite linear complementarity problems based on the Kojima-Shindoh-Hara family of directions. Mathematical Programming, 84:39--53, 1999.
Semidefinite and Cone Programming Bibliography/Comments - Wolkowicz (2004) (Correct)
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R.D.C. MONTEIRO and T. TSUCHIYA. Polynomiality of primal-dual algorithms for semidefinite linear complementarity problems based on the Kojima-Shindoh-Hara family of directions. Math. Programming, 84:39--53, 1999.
Algorithms and Software for LMI Problems in Control - Vandenberghe, Balakrishnan (1997) (3 citations) (Correct)
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R. D. C. Monteiro and T. Tsuchiya, "Polynomiality of primal-dual algorithms for semidefinite linear complementarity problems based on the Kojima-Shindoh-Hara family of directions", Technical report, School of Industrial and Systems Engineering. Georgia Institute of Technology, 1996. 14
Search Directions in the SDP and the Monotone SDLCP.. - Kojima (1997) (7 citations) (Correct)
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R.D.C. Monteiro and T. Tsuchiya. Polynomiality of primal-dual algorithms for semidefinite linear complementarity problems based on the Kojima-Shindoh-Hara family of directions. Technical report, School of Industrial and Systems Engineering, Georgia Tech. USA, 1996.
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