A nonmonotone trust-region line search method for large-scale unconstrained optimization |
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Authors: | Masoud Ahookhosh Mohammad Reza Peyghami |
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Affiliation: | a Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran b Department of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran |
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Abstract: | We consider an efficient trust-region framework which employs a new nonmonotone line search technique for unconstrained optimization problems. Unlike the traditional nonmonotone trust-region method, our proposed algorithm avoids resolving the subproblem whenever a trial step is rejected. Instead, it performs a nonmonotone Armijo-type line search in direction of the rejected trial step to construct a new point. Theoretical analysis indicates that the new approach preserves the global convergence to the first-order critical points under classical assumptions. Moreover, superlinear and quadratic convergence are established under suitable conditions. Numerical experiments show the efficiency and effectiveness of the proposed approach for solving unconstrained optimization problems. |
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Keywords: | Unconstrained optimization Trust-region method Armijo-type line search Nonmonotone technique |
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