On the Local Convergence of a Predictor-Corrector Method for Semidefinite Programming

Type: Article

Publication Date: 1999-01-01

Citations: 26

DOI: https://doi.org/10.1137/s1052623497316828

Abstract

We study the local convergence of a predictor-corrector algorithm for semidefinite programming problems based on the Monteiro--Zhang unified direction whose polynomial convergence was recently established by Monteiro. Under strict complementarity and nondegeneracy assumptions superlinear convergence with Q-order 1.5 is proved if the scaling matrices in the corrector step have bounded condition number. A version of the predictor-corrector algorithm enjoys quadratic convergence if the scaling matrices in both predictor and corrector steps have bounded condition numbers. The latter results apply in particular to algorithms using the Alizadeh--Haeberly--Overton (AHO) direction since there the scaling matrix is the identity matrix.

Locations

  • CiteSeer X (The Pennsylvania State University) - View - PDF
  • SIAM Journal on Optimization - View

Similar Works

Action Title Year Authors
+ PDF Chat On a general class of interior-point algorithms for semidefinite programming with polynomial complexity and superlinear convergence 1999 Jun Ji
Florian A. Potra
Rongqin Sheng
+ Superlinear Convergence 2000 Hans Frenk
C. Roos
TamĂĄs Terlaky
Shuzhong Zhang
+ Polynomial Convergence of Primal-Dual Algorithms for Semidefinite Programming Based on the Monteiro and Zhang Family of Directions 1998 Renato D. C. Monteiro
+ A Note on the Local Convergence of a Predictor-Corrector Interior-Point Algorithm for the Semidefinite Linear Complementarity Problem Based on the Alizadeh--Haeberly--Overton Search Direction 2005 Zhaosong Lu
Renato D. C. Monteiro
+ A predictor-corrector algorithm for semidefinite programming that uses the factor width cone 2023 Felix Kirschner
Etienne de Klerk
+ An Implementable Predictor-Corrector Method for Solving Semidefinite Programming Problems 2014 Rupaj Kumar Nayak
M. P. Biswal
S. Padhy
+ On the superlinear local convergence of a penalty-free method for nonlinear semidefinite programming 2016 Qi Zhao
Zhongwen Chen
+ A New Second-Order Mehrotra-Type Predictor-Corrector Algorithm for SDO 2016 Huang
Fangyan
Zhang
Mingwang
Zhengwei
+ On Mehrotra-Type Predictor-Corrector Algorithm for Convex Quadratic Programming 2009 Mingwang Zhang
+ A finite termination mehrotra-type predictor-corrector algorithm for Semidefinite Optimization 2010 Mingwang Zhang
Huaping Chen
Weihua Li
+ Predictor-corrector method for linear complementarity problems with polynomial complexity and superlinear convergence 1995 Jun Ji
Florian A. Potra
Shuqiang Huang
+ POLYNOMIAL CONVERGENCE OF PREDICTOR-CORRECTOR ALGORITHMS FOR SDLCP BASED ON THE M-Z FAMILY OF DIRECTIONS 2011 Feixiang Chen
Ruiyin Xiang
+ Polynomial Convergence of Predictor-Corrector for SDLCP Based on the M-Z Family of Directions 2011 Feixiang Chen
Zhanfei Zuo
+ High accuracy algorithms for the solutions of semidefinite linear programs 2001 Henry Wolkowicz
Serge Kruk
+ A second order Mehrotra-type predictor-corrector algorithm for semidefinite optimization 2012 Mingwang Zhang
+ On long-step predictor-corrector interior-point algorithm for semidefinite programming with Monteiro-Zhang unified search directions 1999 Masayuki Shida
+ New complexity analysis of a Mehrotra-type predictor–corrector algorithm for semidefinite programming 2012 Hongwei Liu
Changhe Liu
Ximei Yang
+ Convergence failures of the Burer-Monteiro factorization algorithm 2020 Maurits Brinkman
+ PDF Chat A Note on Convergence Analysis of an SQP-Type Method for Nonlinear Semidefinite Programming 2008 Yun Wang
Shao‐Wu Zhang
Liwei Zhang
+ PDF Chat A Low-Rank ADMM Splitting Approach for Semidefinite Programming 2024 Qiushi Han
Chenxi Li
Zhenwei Lin
Caihua Chen
Qi Deng
Dongdong Ge
Huikang Liu
Yinyu Ye

Works That Cite This (26)

Action Title Year Authors
+ PDF Chat Strong duality and minimal representations for cone optimization 2012 Levent Tunçel
Henry Wolkowicz
+ Local Superlinear Convergence of Polynomial-Time Interior-Point Methods for Hyperbolicity Cone Optimization Problems 2016 Yu. Nesterov
Levent Tunçel
+ PDF Chat A study of search directions in primal-dual interior-point methods for semidefinite programming 1999 Mike Todd
+ A new<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msqrt><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msqrt><mml:mi>L</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-iteration predictor–corrector algorithm with wide neighborhood for semidefinite programming 2013 Zengzhe Feng
Liang Fang
+ Generating and measuring instances of hard semidefinite programs 2008 H. Wei
Henry Wolkowicz
+ Polynomial Convergence of a New Family of Primal-Dual Algorithms for Semidefinite Programming 1999 Renato D. C. Monteiro
Takashi Tsuchiya
+ PDF Chat Asymptotic Behavior of Underlying NT Paths in Interior Point Methods for Monotone Semidefinite Linear Complementarity Problems 2010 Chee-Khian Sim
+ PDF Chat Study of a Logarithmic Barrier Approach for Linear Semidefinite Programming 2018 Assma Leulmi
+ Non-Interior continuation methods for solving semidefinite complementarity problems 2003 Xin Chen
Paul Tseng
+ A Full Nesterov–Todd Step Infeasible Interior-Point Method for Second-Order Cone Optimization 2013 M. Zangiabadi
G. Gu
C. Roos