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Abstract
In this paper, aiming at the unconstrained optimization problem, a new nonmonotone adaptive retrospective trust region line search method is presented, which takes advantages of multidimensional filter technique to increase the acceptance probability of the trial step. The new nonmonotone trust region ratio is presented, which based on the convex combination of nonmonotone trust region ratio and retrospective ratio. The global convergence and the superlinear convergence of the algorithm are shown in the right circumstances. Comparative numerical experiments show the better effective and robustness.
Highlights
Consider the following unconstrained optimization problem min f ðxÞ ð1Þ x2Rn where f:Rn!R is a twice continuously differentiable function
The basic idea of trust region method as follows: at the iteration point xk, the trial step dk is obtained by solving the subproblem
It is worth mentioning that Gould et al [17] proposed an algorithm by using filter technique for unconstrained optimization problems, the main idea is to accept the new iteration point as much as possible
Summary
Consider the following unconstrained optimization problem min f ðxÞ ð1Þ x2Rn where f:Rn!R is a twice continuously differentiable function. The basic idea of trust region method as follows: at the iteration point xk, the trial step dk is obtained by solving the subproblem. RBk is negative or positive but not close to 1, Δk is decreased and the subproblem should be resolved It is well-known that monotone techniques may lead to the rate of convergence slows down, especially in the presence of the narrow curved valley, and the objective function is required to be decreased at each iteration. The filter is able to reject poor trial iterates and enforce global convergence from arbitrary starting points In this case, it is worth mentioning that Gould et al [17] proposed an algorithm by using filter technique for unconstrained optimization problems, the main idea is to accept the new iteration point as much as possible.
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