Convergence analysis of a nonlinear Lagrangian method for nonconvex semidefinite programmingwith subproblem inexactly solved

Yang Li; Yonghong Ren; Yun Wang; Jian Gu

doi:10.3934/jimo.2015.11.65

Article Contents

2015, Volume 11, Issue 1: 65-81. Doi: 10.3934/jimo.2015.11.65

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Convergence analysis of a nonlinear Lagrangian method for nonconvex semidefinite programming with subproblem inexactly solved

1.
School of Science, Dalian Nationalities University, Dalian, 116600
2.
School of Mathematics, Liaoning Normal University, Dalian, 116029
3.
College of Information Science and Engineering, Shandong Agricultural University, Taian, 271018
4.
School of Science, Dalian Ocean University, Dalian, 116023

Received: July 31, 2012

Revised: November 30, 2013

Published: December 2014

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Abstract

In this paper, we analyze the convergence properties of a nonlinear Lagrangian method based on Log-Sigmoid function for nonconvex semidefinite programming (NCSDP) problems. It is different from other convergence analysis, because the subproblem in our algorithm is inexactly solved. Under the constraint nondegeneracy condition, the strict complementarity condition and the second order sufficient conditions, it is obtained that the nonlinear Lagrangian algorithm proposed is locally convergent by choosing a proper stopping criterion and the error bound of solution is proportional to the penalty parameter when the penalty parameter is less than a threshold.

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Mathematics Subject Classification: Primary: 90C22, 90C26; Secondary: 90C30.

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