Abstract
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 nommonotone 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.
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This work was supported by the National Natural Science Foundation of China (Grant No. 10171055).
Zhensheng Yu received his BS from Qufu Normal University in 2001. He is now a docterate student in Dalian University of Technology. His research intrests cover optimization theory and algorithm.
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Yu, Z., Wang, C. & Yu, J. Combining trust region and linesearch algorithm for equality constrained optimization. JAMC 14, 123–136 (2004). https://doi.org/10.1007/BF02936103
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DOI: https://doi.org/10.1007/BF02936103