Generalized monotone line search SQP algorithm for constrained minimax problems

Authors: Jian, Jin-Bao¹; Zhang, Xue-Lu²; Quan, Ran³; Ma, Qing⁴

Source: Optimization, Volume 58, Number 1, January 2009 , pp. 101-131(31)

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Abstract:

In this article, non-linear minimax problems with general constraints are discussed. By means of solving one quadratic programming an improved direction is yielded and a second-order correction direction can also be at hand via one system of linear equations. So a new algorithm for solving the discussed problems is presented. In connection with a special merit function, the generalized monotone line search is used to yield the step size at each iteration. Under mild conditions, we can ensure global and superlinear convergence. Finally, some numerical experiments are operated to test our algorithm, and the results demonstrate that it is promising.

Keywords: constrained minimax problems; generalized monotone line search; SQP algorithm; global convergence; superlinear convergence

Document Type: Research article

DOI: http://dx.doi.org/10.1080/02331930801951140

Affiliations: 1: College of Mathematics and Information Science, Guangxi University, Nanning, P.R. China 2: College of Science, Shandong Institute of Light Industry, Jinan, P.R. China 3: College of Electrical Engineering, Guangxi University, P.R. China 4: Chinese Women's College Shandong Branch, Jinan, P.R. China

Publication date: 2009-01-01