Piecewise concavity and discrete approaches to continuous minimax problems

2000 ◽  
pp. 511-524 ◽  
Author(s):  
Fabio Tardella
Keyword(s):  
Minimax Problems ◽  
Continuous Minimax

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.

Some Linear Minimax Problems Over an Ordered Field

1955 ◽  
Vol 77 (3) ◽  
pp. 541
Author(s):  
R. J. Levit
Keyword(s):  
Minimax Problems ◽  
Ordered Field
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