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A modified trust region method with arc search

Xin Pan


The main idea of the trust region method for unconstrained optimization is to find a neighborhood named “trust region” around the current point in which a quadratic model agrees with the objective function, and to search a better point in the region based on the quadratic model. When the objective function is very nonlinear, the radius of trust region may be very small and too many steps should be taken to search the minimizer. In order to efficiently solve the unconstrained optimization problem in which the objective function is very nonlinear, a modified trust region framework is proposed in this paper. A procedure called “arc search” is introduced to improve the trial step, and a new strategy to adjust the trust region radius is proposed which prevents the radius from being too small. The global convergence of this new method is proved in this paper under some mild assumptions. Numerical tests illustrate that this new method is more efficient than the traditional trust region method.


unconstrained optimization; trust region method; arc search; numerical experiments.

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