• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.971-980
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• 2012

In this paper, a method associating with one new form of nonmonotone linesearch technique is proposed, which can be regarded as a generalization of the Perry-Shanno memoryless quasi-Newton type method. Under some reasonable conditions, the global convergence of the proposed method is proven. Numerical tests show its efficiency.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.123-136
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• 2004

In this paper, a combining trust region and line search algorithm for equality constrained optimization is proposed. At each iteration, we only need to solve the trust region subproblem once, when the trust region trial step can not be accepted, we switch to line search to obtain the next iteration. Hence, the difficulty of repeated solving trust region subproblem in an iterate is avoided. In order to allow the direction of negative curvature, we add second correction step in trust region step and employ nonmonotone technique in line search. The global convergence and local superlinearly rate are established under certain assumptions. Some numerical examples are given to illustrate the efficiency of the proposed algorithm.