A Line Search SQP-type Method with Bi-object Strategy for Nonlinear Semidefinite Programming

We propose a line search exact penalty method with bi-object strategy for nonlinear semidefinite programming. At each iteration, we solve a linear semidefinite programming to test whether the linearized constraints are consistent or not. The search direction is generated by a piecewise quadratic-lin...

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Bibliographic Details
Published in:Acta Mathematicae Applicatae Sinica Vol. 38; no. 2; pp. 388 - 409
Main Authors: Fu, Wen-hao, Chen, Zhong-wen
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2022
Springer Nature B.V
Edition:English series
Subjects:
Algorithms
Applications of Mathematics
Iterative methods
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Penalty function
Search methods
Semidefinite programming
Theoretical
rate of convergence
bi-object strategy
49M30
nonlinear semidefinite programming
global convergence
90C22
ISSN:0168-9673, 1618-3932
Online Access:Get full text
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Summary:We propose a line search exact penalty method with bi-object strategy for nonlinear semidefinite programming. At each iteration, we solve a linear semidefinite programming to test whether the linearized constraints are consistent or not. The search direction is generated by a piecewise quadratic-linear model of the exact penalty function. The penalty parameter is only related to the information of the current iterate point. The line search strategy is a penalty-free one. Global and local convergence are analyzed under suitable conditions. We finally report some numerical experiments to illustrate the behavior of the algorithm on various degeneracy situations.
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ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-022-1081-9