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A nonmonotone trust-region line search method for large-scale unconstrained optimization. (English) Zbl 1236.90077
Summary: 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.

MSC:
90C06 Large-scale problems in mathematical programming
90C55 Methods of successive quadratic programming type
90C26 Nonconvex programming, global optimization
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