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Abstract: We present a unified analysis for a class of long-step primal-dual path-following algorithms for semidefinite programming whose search directions are obtained through linearization of the symmetrized equation of the central path HP (XS) j [P XSP \Gamma1 + (PXSP \Gamma1 ) T ]=2 = ¯I, introduced by Zhang. At an iterate (X; S), we choose a scaling matrix P from the class of nonsingular matrices P such that PXSP \Gamma1 is symmetric. This class of matrices includes the three well-known... (Update)
Context of citations to this paper: More
...and step lengths, and does not add any equality constraints in the original SDP formulation. Various search directions [1, 13, 15, 16, 20, 21, 24, 27] have been proposed so far for primal dual interior point methods. Among others, we restrict ourselves to the HRVW KSH M...
...as perturbed Newton s methods applied to (4.24a) 4.24b) 4.25) Examples of symmetrizations (4. 25) include the Monteiro Zhang family [15], in which Theta(X; S) HP (XS) where HP (M ) 1 2 Theta PMP Gamma1 (PMP Gamma1 ) T ; with a given a nonsingular matrix P...
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BibTeX entry: (Update)
R.D.C. MONTEIRO and Y. ZHANG. A unified analysis for a class of longstep primal-dual path-following interior-point algorithms for semidefinite programming. Math. Programming, 81(3, Ser. A):281--299, 1998. http://citeseer.ist.psu.edu/monteiro98unified.html More
@article{ monteiro98unified,
author = "R. D. C. {MONTEIRO} and Y. {ZHANG}",
title = "A unified analysis for a class of long-step primal-dual path-following interior-point algorithms for semidefinite programming",
volume = "81",
number = "3, Ser. A",
pages = "281--299",
year = "1998",
url = "citeseer.ist.psu.edu/monteiro98unified.html" }
Citations (may not include all citations):326 Topics in Matrix Analysis (context) - Horn, Johnson - 1991
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. - 1996
142 Primal-dual interior-point methods for self-scaled cones - Nesterov, Todd - 1997
121 Self-scaled barriers and interior-point methods for convex p.. (context) - Nesterov, Todd - 1995
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
78 Interior-point methods for the monotone semidefinite linear .. (context) - Kojima, Shindoh et al. - 1997
60 Combinatorial optimization with interior point methods and s.. (context) - Alizadeh - 1991
55 Symmetric primal-dual path-following algorithms for semidefi.. - Sturm, Zhang - 1995
49 An interior-point method for minimizing the maximum eigenval.. (context) - Jarre - 1993
48 Self-concordant functions and polynomial time methods in con.. (context) - Nesterov, Nemirovskii - 1989
47 A superlinearly convergent primal-dual infeasible-interior-p.. - Potra, Sheng - 1995
40 Superlinear convergence of a symmetric primal-dual path-foll.. - Luo, Sturm et al. - 1996
39 Polynomial convergence of primal-dual algorithms for semidef.. - Monteiro - 1996
34 On extending some primal-dual interior-Point algorithms from.. - Zhang - 1995
30 A primal-dual interior point method for linear programming (context) - Kojima, Mizuno et al. - 1989
30 Local convergence of predictor-corrector infeasibleinterior .. - Kojima, Shida et al. - 1995
27 Existence of search directions in interior-point algorithms .. - Shida, Shindoh et al. - 1996
21 Interior Point Methods in Convex Programming: Theory and App.. (context) - Nesterov, Nemirovskii - 1994
20 Optimization over positive semidefinite matrices: Mathematic.. (context) - Nesterov, Nemirovskii - 1990
17 A predictor-corrector method for semi-definite programming (context) - Lin, Saigal - 1995
14 A class of projective transformations for linear programming (context) - Ye - 1990
8 A note on the Nesterov-Todd and the Kojima-ShindohHara searc.. - Kojima, Shida et al. - 1996
8 A general approach to the design of optimal methods for smoo.. (context) - Nesterov, Nemirovskii - 1988
3 the long-step path-following method for semidefinite program.. - Sturm, Zhang - 1996
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