On the long-step path-following method for semidefinite programming

Authors:
Jos F. Sturm;Shuzhong Zhang
Affiliations:
Tinbergen Institute Rotterdam, Netherlands;Erasmus University Rotterdam, Econometric Institute, P.O. Box 1738, 3000 DR Rotterdam, Netherlands
Venue:
Operations Research Letters
Year:
1998

Citing 6
Cited 0

A primal-dual interior point algorithm for linear programming

Progress in Mathematical Programming Interior-point and related methods
On adaptive-step primal-dual interior-point algorithms for linear programming

Mathematics of Operations Research
Self-scaled barriers and interior-point methods for convex programming

Mathematics of Operations Research
Interior-Point Methods for the Monotone Semidefinite Linear Complementarity Problem in Symmetric Matrices

SIAM Journal on Optimization
Primal--Dual Path-Following Algorithms for Semidefinite Programming

SIAM Journal on Optimization
Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results

Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results

Quantified Score

Hi-index	0.00

Visualization

Abstract

It has been shown in various recent research reports that the analysis of short-step primal-dual path following algorithms for linear programming can be nicely generalized to semidefinite programming. However, the analysis of long-step path-following algorithms for semidefinite programming appeared to be less straightforward. For such an algorithm, Monteiro (1997) obtained an O(n^1^.^5log(1/@e)) iteration bound for obtaining an @e-optimal solution, where n is the order of the semidefinite decision variable. In this paper, we propose to use a different search direction, viz. the so-called V-space direction. It is shown that this modification reduces the iteration complexity to O(nlog(1/@e)). Independently, Monteiro and Y. Zhang obtained a similar result using Nesterov-Todd directions.