$${\cal U}{\cal V}$$-theory of a Class of Semidefinite Programming and Its Applications

2021 ◽  
Vol 37 (4) ◽  
pp. 717-737
Author(s):  
Ming Huang ◽  
Jin-long Yuan ◽  
Li-ping Pang ◽  
Zun-quan Xia
Keyword(s):  
Semidefinite Programming

scholarly journals Towards a computational proof of Vizing's conjecture using semidefinite programming and sums-of-squares

2021 ◽  
Vol 107 ◽  
pp. 67-105
Author(s):  
Elisabeth Gaar ◽  
Daniel Krenn ◽  
Susan Margulies ◽  
Angelika Wiegele
Keyword(s):  
Semidefinite Programming ◽  
Sums Of Squares

scholarly journals Data-driven Linear Quadratic Regulation via Semidefinite Programming

2020 ◽  
Vol 53 (2) ◽  
pp. 3995-4000
Author(s):  
Monica Rotulo ◽  
Claudio De Persis ◽  
Pietro Tesi
Keyword(s):  
Semidefinite Programming ◽  
Data Driven ◽  
Linear Quadratic ◽  
Linear Quadratic Regulation

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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