A note on solving nonlinear minimax problems via a differentiable penalty function

1985 ◽  
Vol 46 (1) ◽  
pp. 95-103 ◽  
Author(s):  
D. F. Shanno ◽  
L. Whitaker
Keyword(s):  
Penalty Function ◽  
Minimax Problems ◽  
Nonlinear Minimax Problems ◽  
Nonlinear Minimax

scholarly journals A QP-Free Algorithm for Finite Minimax Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Daolan Han ◽  
Jinbao Jian ◽  
Qinfeng Zhang
Keyword(s):  
Minimax Problems ◽  
Linear Equations ◽  
Inequality Constraints ◽  
Coefficient Matrix ◽  
Systems Of Linear Equations ◽  
Full Dimension ◽  
Finite Minimax ◽  
The Stability ◽  
Nonlinear Minimax Problems ◽  
Nonlinear Minimax

The nonlinear minimax problems without constraints are discussed. Due to the expensive computation for solving QP subproblems with inequality constraints of SQP algorithms, in this paper, a QP-free algorithm which is also called sequential systems of linear equations algorithm is presented. At each iteration, only two systems of linear equations with the same coefficient matrix need to be solved, and the dimension of each subproblem is not of full dimension. The proposed algorithm does not need any penalty parameters and barrier parameters, and it has small computation cost. In addition, the parameters in the proposed algorithm are few, and the stability of the algorithm is well. Convergence property is described and some numerical results are provided.

scholarly journals Generalised monotone line search algorithm for degenerate nonlinear minimax problems

2006 ◽  
Vol 73 (1) ◽  
pp. 117-127 ◽  
Author(s):  
Jin-Bao Jian ◽  
Ran Quan ◽  
Xue-Lu Zhang
Keyword(s):  
Quadratic Programming ◽  
Line Search ◽  
Regularity Condition ◽  
Search Algorithm ◽  
Minimax Problems ◽  
Search Technique ◽  
Line Search Technique ◽  
Nonlinear Minimax Problems ◽  
Line Search Algorithm ◽  
Nonlinear Minimax

In this paper, nonlinear minimax problems are discussed. Using Sequential Quadratic Programming and the generalised monotone line search technique, we propose a new algorithm for solving degenerate minimax problems. At each iteration of the proposed algorithm, a search direction is obtained by solving a new Quadratic Programming problem which always has a solution. Global convergence can be obtained without the regularity condition of linear independence. Finally, some numerical experiments are reported.

Quadratically constraint quadratical algorithm model for nonlinear minimax problems

2008 ◽  
Vol 205 (1) ◽  
pp. 247-262 ◽  
Author(s):  
Mian-Tao Chao ◽  
Zhong-Xing Wang ◽  
Yu-Mei Liang ◽  
Qing-Jie Hu
Keyword(s):  
Minimax Problems ◽  
Nonlinear Minimax Problems ◽  
Nonlinear Minimax
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