scholarly journals An SQP Algorithm for Finely Discretized Continuous Minimax Problems and Other Minimax Problems with Many Objective Functions

1996 ◽  
Vol 6 (2) ◽  
pp. 461-487 ◽  
Author(s):  
Jian L. Zhou ◽  
André L. Tits
Keyword(s):  
Minimax Problems ◽  
Objective Functions ◽  
Sqp Algorithm ◽  
Continuous Minimax

scholarly journals An improved SQP algorithm for solving minimax problems

2009 ◽  
Vol 22 (4) ◽  
pp. 464-469 ◽  
Author(s):  
Zhibin Zhu ◽  
Xiang Cai ◽  
Jinbao Jian
Keyword(s):  
Minimax Problems ◽  
Sqp Algorithm

scholarly journals A modified SQP algorithm for minimax problems

2009 ◽  
Vol 360 (1) ◽  
pp. 211-222 ◽  
Author(s):  
Qing-jie Hu ◽  
Yu Chen ◽  
Nei-ping Chen ◽  
Xue-quan Li
Keyword(s):  
Minimax Problems ◽  
Sqp Algorithm

An Adaptive Smoothing Method for Continuous Minimax Problems

2015 ◽  
Vol 32 (01) ◽  
pp. 1540001
Author(s):  
Hongxia Yin
Keyword(s):  
Minimax Problems ◽  
Minimax Problem ◽  
Descent Method ◽  
Smoothing Parameter ◽  
Smoothing Method ◽  
Steepest Descent Method ◽  
Adaptive Smoothing ◽  
Ill Conditioning ◽  
Quasi Newton ◽  
Continuous Minimax

A simple and implementable two-loop smoothing method for semi-infinite minimax problem is given with the discretization parameter and the smoothing parameter being updated adaptively. We prove the global convergence of the algorithm when the steepest descent method or a BFGS type quasi-Newton method is applied to the smooth subproblems. The strategy for updating the smoothing parameter can not only guarantee the convergence of the algorithm but also considerably reduce the ill-conditioning caused by increasing the value of the smoothing parameter. Numerical tests show that the algorithm is robust and effective.

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