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Volumn 23, Issue 1-2, 1998, Pages 53-61

A long-step primal - Dual path-following method for semidefinite programming

Author keywords

Logarithmic barrier function; Primal dual interior point methods; Proximity measure; Semidefinite programming

Indexed keywords

ALGORITHMS; ITERATIVE METHODS; OPTIMIZATION; PROBLEM SOLVING;

EID: 0032131673     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6377(98)00018-2     Document Type: Article
Times cited : (4)

References (25)
  • 1
    • 0003169116 scopus 로고
    • Interior point methods in semidefinite programming with applications to combinatorial optimization problems
    • F. Alizadeh, Interior point methods in semidefinite programming with applications to combinatorial optimization problems, SIAM J. Optim. 5 (1995) 13-51.
    • (1995) SIAM J. Optim. , vol.5 , pp. 13-51
    • Alizadeh, F.1
  • 4
    • 0027694147 scopus 로고
    • A long step barrier method for convex quadratic programming
    • K. Anstreicher, D. den Hertog, C. Roos, T. Terlaky, A long step barrier method for convex quadratic programming, Algorithmica 10 (1993) 365-382.
    • (1993) Algorithmica , vol.10 , pp. 365-382
    • Anstreicher, K.1    Den Hertog, D.2    Roos, C.3    Terlaky, T.4
  • 5
    • 0003606513 scopus 로고
    • Quadratic and Convex Programming Kluwer Academic Publishers, Dordrecht
    • D. Den Hertog, Interior Point Approach to Linear, Quadratic and Convex Programming Kluwer Academic Publishers, Dordrecht, 1994.
    • (1994) Interior Point Approach to Linear
    • Den Hertog, D.1
  • 6
    • 3643136854 scopus 로고
    • On a matrix generalization of affine-scaling vector fields
    • L. Faybusovich, On a matrix generalization of affine-scaling vector fields, SIAM J. Matrix Anal. Appl. 16 (1995) 886-897.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 886-897
    • Faybusovich, L.1
  • 7
    • 33744627181 scopus 로고
    • Semi-definite programming: A path-following algorithm for linear-quadratic functional
    • Technical Report, Department of Mathematics, University of Notre Dame, Notre Dame, IN, USA, to appear
    • L. Faybusovich, Semi-definite programming: a path-following algorithm for linear-quadratic functional, Technical Report, Department of Mathematics, University of Notre Dame, Notre Dame, IN, USA, 1995; SIAM J. Optim., to appear.
    • (1995) SIAM J. Optim.
    • Faybusovich, L.1
  • 11
    • 0028530911 scopus 로고
    • Primal-dual algorithms for linear programming based on the logarithmic barrier method
    • B. Jansen, C. Roos, T. Terlaky, J.P. Vial, Primal-dual algorithms for linear programming based on the logarithmic barrier method, J. Optim. Theory Appl. 83 (1994) 1-26.
    • (1994) J. Optim. Theory Appl. , vol.83 , pp. 1-26
    • Jansen, B.1    Roos, C.2    Terlaky, T.3    Vial, J.P.4
  • 12
    • 33744562367 scopus 로고    scopus 로고
    • A logarithmic barrier Newton method for semidefinite programming
    • J. Jiang, M. Shi, A logarithmic barrier Newton method for semidefinite programming, Systems Sci. Math. Sci. 10 (1997) 168-175.
    • (1997) Systems Sci. Math. Sci. , vol.10 , pp. 168-175
    • Jiang, J.1    Shi, M.2
  • 16
    • 0010763670 scopus 로고
    • Technical Report 1125, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York
    • Y. Nesterov, M.J. Todd, Primal-dual interior-point methods for self-scaled cones, Technical Report 1125, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York, 1995.
    • (1995) Primal-dual Interior-point Methods for Self-scaled Cones
    • Nesterov, Y.1    Todd, M.J.2
  • 17
    • 0001110772 scopus 로고
    • On minimizing the maximum eigenvalue of a symmetric matrix
    • M.L. Overton, On minimizing the maximum eigenvalue of a symmetric matrix, SIAM J. Matrix Anal. Appl. 9 (1988) 256-268.
    • (1988) SIAM J. Matrix Anal. Appl. , vol.9 , pp. 256-268
    • Overton, M.L.1
  • 19
    • 0003133787 scopus 로고
    • Long steps with the logarithmic penalty barrier function
    • J. Gabszevwicz, J.-F. Richard, L. Wolsey (Eds.), (dedicated to Jacques H. Drèze), Elsevier Science Publishers, Amsterdam
    • C. Roos, J.-Ph. Vial, Long steps with the logarithmic penalty barrier function, in: J. Gabszevwicz, J.-F. Richard, L. Wolsey (Eds.), Economic Decision-Making: Games, Economics and Optimization (dedicated to Jacques H. Drèze), Elsevier Science Publishers, Amsterdam, 1990, pp. 433-441.
    • (1990) Economic Decision-Making: Games, Economics and Optimization , pp. 433-441
    • Roos, C.1    Vial, J.-Ph.2
  • 20
    • 0026838852 scopus 로고
    • A polynomial method of approximate centers for linear programming
    • C. Roos, J.-Ph. Vial, A polynomial method of approximate centers for linear programming, Math. Programming 54 (1992) 295-306.
    • (1992) Math. Programming , vol.54 , pp. 295-306
    • Roos, C.1    Vial, J.-Ph.2
  • 23
    • 0029338589 scopus 로고
    • A primal-dual potential reduction method for problems involving matrix inequalities
    • L. Vandenberghe, S. Boyd, A primal-dual potential reduction method for problems involving matrix inequalities, Math. Programming 69 (1995) 205-236.
    • (1995) Math. Programming , vol.69 , pp. 205-236
    • Vandenberghe, L.1    Boyd, S.2
  • 24
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • L. Vandenberghe, S. Boyd, Semidefinite programming, SIAM Rev. 38 (1996) 49-95.
    • (1996) SIAM Rev. , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.