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Incorporating nonmonotone strategies into the trust region method for unconstrained optimization. (English) Zbl 1183.90387
Summary: This paper concerns a nonmonotone line search technique and its application to the trust region method for unconstrained optimization problems. In our line search technique, the current nonmonotone term is a convex combination of the previous nonmonotone term and the current objective function value, instead of an average of the successive objective function values that was introduced by H. Zhang and W. W. Hager [SIAM J. Optim. 14, No. 4, 1043–1056 (2004; Zbl 1073.90024)]. We incorporate this nonmonotone scheme into the traditional trust region method such that the new algorithm possesses nonmonotonicity. Unlike the traditional trust region method, our algorithm performs a nonmonotone line search to find a new iteration point if a trial step is not accepted, instead of resolving the subproblem. Under mild conditions, we prove that the algorithm is global and superlinear convergence holds. Primary numerical results are reported.

90C30 Nonlinear programming
Full Text: DOI
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