A parametric embedding for the finite minimax problem

1999 ◽  
Vol 49 (3) ◽  
pp. 359-371 ◽  
Author(s):  
Guillermo L�pez ◽  
Francisco Guerra
Keyword(s):  
Minimax Problem ◽  
Finite Minimax ◽  
Parametric Embedding

scholarly journals A new three-term conjugate gradient method for solving the finite minimax problems

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 737-758
Author(s):  
Yue Hao ◽  
Shouqiang Du ◽  
Yuanyuan Chen
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problem ◽  
Minimax Problems ◽  
Minimax Problem ◽  
Constrained Optimization Problem ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient ◽  
Finite Minimax

In this paper, we consider the method for solving the finite minimax problems. By using the exponential penalty function to smooth the finite minimax problems, a new three-term nonlinear conjugate gradient method is proposed for solving the finite minimax problems, which generates sufficient descent direction at each iteration. Under standard assumptions, the global convergence of the proposed new three-term nonlinear conjugate gradient method with Armijo-type line search is established. Numerical results are given to illustrate that the proposed method can efficiently solve several kinds of optimization problems, including the finite minimax problem, the finite minimax problem with tensor structure, the constrained optimization problem and the constrained optimization problem with tensor structure.

A smooth method for the finite minimax problem

1993 ◽  
Vol 60 (1-3) ◽  
pp. 187-214 ◽  
Author(s):  
G. Di Pillo ◽  
L. Grippo ◽  
S. Lucidi
Keyword(s):  
Minimax Problem ◽  
Finite Minimax

scholarly journals A Simple SQP Algorithm for Constrained Finite Minimax Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Lirong Wang ◽  
Zhijun Luo
Keyword(s):  
Quadratic Programming ◽  
Minimax Problems ◽  
Minimax Problem ◽  
Auxiliary Variable ◽  
Mild Conditions ◽  
Global And Superlinear Convergence ◽  
Sequential Quadratic Programming Method ◽  
Finite Minimax ◽  
Quadratic Programming Method ◽  
Constrained Minimax

A simple sequential quadratic programming method is proposed to solve the constrained minimax problem. At each iteration, through introducing an auxiliary variable, the descent direction is given by solving only one quadratic programming. By solving a corresponding quadratic programming, a high-order revised direction is obtained, which can avoid the Maratos effect. Furthermore, under some mild conditions, the global and superlinear convergence of the algorithm is achieved. Finally, some numerical results reported show that the algorithm in this paper is successful.

Variable Programming: A Generalized Minimax Problem. Part II: Algorithms

2005 ◽  
Vol 30 (3) ◽  
pp. 263-295 ◽  
Author(s):  
Yong-Chang Jiao ◽  
Yee Leung ◽  
Zongben Xu ◽  
Jiang-She Zhang
Keyword(s):  
Minimax Problem
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