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Abstract: We consider a family of primal/primal-dual/dual search directions for the monotone LCP over the space of n \Theta n symmetric block-diagonal matrices. We consider two infeasible predictor-corrector path-following methods using these search directions, with the predictor and corrector steps used either in series (similar to the Mizuno-Todd-Ye method) or in parallel (similar to Mizuno et al./McShane's method). The methods attain global linear convergence with a convergence ratio which, depending... (Update)
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.... on extending the interior point approach to SDLP (see [1, 2, 29, 31, 34, 35, 38, 47] and references therein) and, to monotone SDLCP [29, 44] and to semidefinite (nonlinear) complementarity problems (SDCP) 39] Recently, extensions of the merit function approach have also...
.... Monteiro and Zhang [18] Nesterov and Nemirovskii [21] Nesterov and Todd [24, 23] Potra and Sheng [25] Sturm and Zhang [26] Tseng [28], Vandenberghe and Boyd [29] and Zhang [31] Most of these more recent works are concentrated on primal dual methods. The first algorithms...
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BibTeX entry: (Update)
P. Tseng. Search directions and convergence analysis of some infeasible pathfllowing methods for the monotone semi-definite LCP. Technical Report , Department of Mathemaics, University of Washington, Seatle, WA 98195, 1996. http://citeseer.ist.psu.edu/tseng96search.html More
@article{ tseng98search,
author = "P. Tseng",
title = "Search Directions and Convergence Analysis of Some Infeasible Path-following Methods for the Monotone Semi-Definite {LCP}",
journal = "Optimization Methods and Software",
volume = "9",
pages = "245--268",
year = "1998",
url = "citeseer.ist.psu.edu/tseng96search.html" }
Citations (may not include all citations):307 Interior Point Polynomial Methods in Convex Programming: The.. (context) - Nesterov, Nemirovskii - 1993
258 Matrix Analysis (context) - Horn, Johnson - 1985
230 Interior point methods in semidefinite programming with appl.. - Alizadeh - 1995
173 An interior-point method for semidefinite programming - Helmberg, Rendl et al. - 1996
146 Primal-dual interior point methods for semidefinite programm.. - Alizadeh, Haeberly et al. - 1994
146 Primal-dual interior point methods for semidefinite programm.. - Alizadeh, Haeberly et al. - 1996
99 Primal-dual path following algorithms for semidefinite progr.. - Monteiro - 1995
92 the Nesterov-Todd direction in semidefinite programming - Todd, Toh et al. - 1996
90 A primal-dual potential reduction method for problems involv.. - Vandenberghe, Boyd - 1995
85 On adaptive step primal-dual interiorpoint algorithms for li.. (context) - Mizuno, Todd et al. - 1993
51 On extending primal-dual interior-point algorithms from line.. - Zhang - 1995
49 An interior-point method for minimizing the maximum eigenval.. (context) - Jarre - 1993
47 A superlinearly convergent primal-dual infeasibleinterior -p.. - Potra, Sheng - 1995
40 A unified analysis for a class of pathfollowing primal-dual .. (context) - Monteiro, Zhang - 1996
40 Superlinear convergence of a symmetric primal-dual path foll.. - Luo, Sturm et al. - 1996
34 A primal-dual infeasible-interiorpoint algorithm for linear .. (context) - Kojima, Megiddo et al. - 1993
27 Existence of search directions in interior-point-algorithms .. - Shida, Shindoh et al. - 1996
25 Complexity of an algorithm for finding an approximate soluti.. (context) - Freund - 1994
25 Self-scaled cones and interior-point methods in nonlinear pr.. - Nesterov, Todd - 1994
24 Homogeneous interior-point algorithms for semidefinite progr.. - Potra, Sheng - 1995
15 A long-step path following algorithm for semidefinite progra.. (context) - Anstreicher, Frampa - 1996
12 A predictor-corrector method for semi-definite linear progra.. - Lin, Saigal - 1995
12 Optimization over the positive-definite cone: interior point.. (context) - Alizadeh - 1992
11 An infeasible start predictor-corrector method for semi-defi.. - Lin, Saigal - 1995
10 Semi-definite programming: a path-following algorithm for a .. (context) - Faybusovich - 1995
10 Polynomiality of infeasible interior point algorithms for li.. (context) - Mizuno - 1994
8 The largest step path following algorithm for monotone linea.. (context) - Gonzaga - 1994
8 Superlinear convergence of interior-point algorithms for sem.. - Potra, Sheng - 1996
8 Practical polynomial time algorithms for linear complementar.. (context) - Mizuno, Yoshise et al. - 1989
7 iteration interior point algorithms for linear programming a.. (context) - McShane, convergent et al. - 1994
5 iteration infeasible predictorcorrector path following metho.. (context) - Tseng, of et al. - 1995
5 Monotone semidefinite complementarity problems - Shida, Shindoh - 1996
3 Shindoh A predictor-corrector interior-point algorithms for .. (context) - Kojima, Shida - 1996
3 Private communication (context) - Todd - 1996
2 Complexity analysis of a linear complementarity algorithm ba.. (context) - Tseng - 1992
2 Shindoh A note on the Nesterov-Todd and the Kojima-Shindo-Ha.. (context) - Kojima, Shida - 1996
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