The rate of convergence of proximal method of multipliers for nonlinear semidefinite programming

Optimization ◽  
2019 ◽  
Vol 69 (4) ◽  
pp. 875-900
Author(s):  
Yule Zhang ◽  
Jia Wu ◽  
Liwei Zhang
Keyword(s):  
Semidefinite Programming ◽  
Rate Of Convergence ◽  
Method Of Multipliers ◽  
Proximal Method ◽  
Nonlinear Semidefinite Programming

A Penalty-Free Method with Trust Region for Nonlinear Semidefinite Programming

2015 ◽  
Vol 32 (01) ◽  
pp. 1540006 ◽  
Author(s):  
Zhongwen Chen ◽  
Shicai Miao
Keyword(s):  
Semidefinite Programming ◽  
Objective Function ◽  
Penalty Function ◽  
Trust Region ◽  
Numerical Results ◽  
New Method ◽  
Penalty Parameter ◽  
Nonlinear Semidefinite Programming ◽  
Globally Convergent ◽  
Nonlinear Objective Function

In this paper, we propose a class of new penalty-free method, which does not use any penalty function or a filter, to solve nonlinear semidefinite programming (NSDP). So the choice of the penalty parameter and the storage of filter set are avoided. The new method adopts trust region framework to compute a trial step. The trial step is then either accepted or rejected based on the some acceptable criteria which depends on reductions attained in the nonlinear objective function and in the measure of constraint infeasibility. Under the suitable assumptions, we prove that the algorithm is well defined and globally convergent. Finally, the preliminary numerical results are reported.

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