Hostname: page-component-7bb8b95d7b-fmk2r Total loading time: 0 Render date: 2024-09-18T16:36:54.119Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalised monotone line search algorithm for degenerate nonlinear minimax problems

Published online by Cambridge University Press:  17 April 2009

Jin-Bao Jian ,
Ran Quan  and
Xue-Lu Zhang
Jin-Bao Jian
Affiliation:
College of Mathematics and Informatics Science, Guangxi University, 530004, Nanning, Peoples Republic of China, e-mail: jianjb@gxu.edu.cn
Ran Quan
Affiliation:
College of Mathematics and Informatics Science, Guangxi University, 530004, Nanning, Peoples Republic of China, e-mail: jianjb@gxu.edu.cn
Xue-Lu Zhang
Affiliation:
College of Mathematics and Informatics Science, Guangxi University, 530004, Nanning, Peoples Republic of China, e-mail: jianjb@gxu.edu.cn
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 73 , Issue 1 , February 2006 , pp. 117 - 127
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Han, S.P., ‘Variable metric methods for minimising a class of nondifferentiable functions’, Math. Programming 20 (1981), 1–13.CrossRefGoogle Scholar
[2]Jian, J.-B. and Tang, C.-M., ‘An SQP feasible descent algorithm for nonlinear inequality constrained optimization without strict complementarity’, Comput. Math. Appl. 49 (2005), 223–238.CrossRefGoogle Scholar
[3]Maratos, N., Exact penalty function algorithm for finite dimensional and control optimization problems, (Ph.D. thesis) (University of London, London UK, 1978).Google Scholar
[4]Panier, E.R. and Tits, A.L., ‘On combining feasibility, descent and superlinear convergence in inequality constrained optimization’, Math. Programming 59 (1993), 261–276.CrossRefGoogle Scholar
[5]Powell, M.J., The convergence of variable metric methods for nonlinearly constrained optimization calculations, (Meyer, R.R. and Robinson, S.M., Editors), Nonlinear Promgramming 3 (Academic Press, New York, 1978).Google Scholar
[6]Vardi, A., ‘New minimax algorithm’, J. Optim. Theory Appl. 75 (1992), 613–634.CrossRefGoogle Scholar
[7]Xue, Y., ‘The sequential quadratic programming method for solving minimax problem’, J. Systems Science Systems Engg. (PRC) 22 (2002), 355–364.Google Scholar
[8]Xue, Y. and Yang, H.Z., ‘Descent algorithm for solving minimax optimization problem’, J. Beijing Plotechnic University 27 (2001), 255–261.Google Scholar
[9]Zhou, J.L. and Tits, A.L., ‘Nonmonotone line search for minimax problems’, J. Optim. Theory Appl. 76 (1993), 455–476.CrossRefGoogle Scholar