On Two Interior-Point Mappings for Nonlinear Semidefinite Complementarity Problems

References

• Alizadeh F. Interior point methods in semidefinite programming with application to combinatorial optimization. SIAM J. Optim. (1995) 5 13 51 Crossref, Google Scholar
• Alizadeh F. , Haeberly J.-P. A. , Overton M. L. Primal-dual interior-point methods for semidefinite programming (1994) . Manuscript presented at the Math Programming Symposium, Ann Arbor Google Scholar
• Alizadeh F. , Haeberly J.-P. A. , Overton M. L. Complementarity and nondegeneracy in semidefinite programming. Math. Programming (1997) 77 111 128 Crossref, Google Scholar
• Ambrosetti A. , Prodi G. A Primer of Nonlinear Analysis (1993) (Cambridge University Press, Cambridge) Google Scholar
• Goldfarb D. , Scheinberg K. Interior point trajectories in semidefinite programming (1996) (Department of Industrial Engineering and Operations Research, Columbia University, New York) . Manuscript Google Scholar
• Kojima M. , Shida M. , Shindoh S. Reduction of monotone linear complementarity problem over cones to linear programs over cones (1995a) . Research report B-296, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan Google Scholar
• Kojima M. , Shida M. , Shindoh S. Local convergence of predictor-corrector infeasible-interior-point algorithms for SDPs and SDLCPs (1995b) . Research report B-306, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan. Math. Programming (to appear) Google Scholar
• Kojima M. , Shida M. , Shindoh S. A predictor-corrector interior-point methods for the semidefinite linear complementarity problem using the Alizadeh-Haeberly-Overton search direction (1996) . Research report B-311, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan Google Scholar
• Kojima M. , Shindoh S. , Hara S. Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices. SIAM J. Optim. (1997) 7 86 125 Crossref, Google Scholar
• Luo Z. Q. , Sturm J. F. , Zhang S. Z. Superlinear convergence of a symmetric primal-dual path following algorithm for semidefinite programming (1996a) (Econometric Institute, Erasmus University, Rotterdam, The Netherlands) . SIAM J. Optim. (to appear) Manuscript Google Scholar
• Luo Z. Q. , Sturm J. F. , Zhang S. Z. Duality and self-duality for conic convex programming (1996b) (Econometric Institute, Erasmus University, Rotterdam, The Netherlands) . Manuscript Google Scholar
• Monteiro R. D. C. Primal-dual path-following algorithms for semidefinite programming. SIAM J. Optim. (1997) 7 663 678 Crossref, Google Scholar
• Monteiro R. D. C. , Pang J. S. Properties of an interior-point mapping for mixed complementarity problems. Math. Oper. Res. (1996) 21 629 654 Link, Google Scholar
• Nesterov Y. E. , Nemirovskii A. S. Interior Point Methods in Convex Programming: Theory and Application (1994) (Society of Industrial and Applied Mathematics, Philadelphia) Crossref, Google Scholar
• Nesterov Y. E. , Todd M. J. Primal-dual interior-point methods for self-scaled cones (1995) . Technical report no. 1125, School of Operations Research and Industrial Engineering, Cornell University, Ithaca. SIAM J. Optim. to appear Google Scholar
• Nesterov Y. E. , Todd M. J. Self-scaled barriers and interior-point methods for convex programming. Math. Oper. Res. (1997) 22 1 42 Link, Google Scholar
• Ortega J. M. , Rheinboldt W. C. Iterative Solution of Nonlinear Equations in Several Variables (1970) (Academic Press, New York) Google Scholar
• Potra F. A. , Sheng R. A superlinearly convergent primal-dual infeasible-interior-point algorithm for semidefinite programming (1995) . Report on Computational Mathematics No. 78, Department of Mathematics, The University of Iowa, Iowa. SIAM J. Optim. to appear Google Scholar
• Ramana M. V. , Tunçel L. , Wolkowicz H. Strong duality for semidefinite programming. SIAM J. Optim. (1997) 7 641 662 Crossref, Google Scholar
• Rockafellar R. T. Convex Analysis (1970) (Princeton University Press, Princeton, New Jersey) Crossref, Google Scholar
• Shapiro A. First and second order analysis of nonlinear semidefinite programs. Math. Programming (1997) 77 301 320 Crossref, Google Scholar
• Shida M. , Shindoh S. Monotone semidefinite complementarity problems (1996) . Research report B-312, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan Google Scholar
• Shida M. , Shindoh S. , Kojima M. Centers of monotone generalized complementarity problems. Math. Oper. Res. (1997) 22 969 976 Link, Google Scholar
• Shida M. , Shindoh S. , Kojima M. Existence of search directions in interior-point algorithms for the SDP and the monotone SDLCP (1996) . Research reports B-310, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan. SIAM J. Optim. to appear Google Scholar
• Vandenberghe L. , Boyd S. Semidefinite programming. SIAM Rev. (1996) 38 49 95 Crossref, Google Scholar
• Zhang Y. On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming (1995) . Technical report 95-20, Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore. SIAM J. Optim. to appear Google Scholar