Adaptive trust-region algorithms for unconstrained optimization. (3rd September 2021) - Rezapour, Mostafa; Asaki, Thomas J.
Abstract : In this paper, we propose two trust-region algorithms for unconstrained optimization. The trust-region algorithms minimize a model of the objective function within the trust-region, next update the size of the region and then repeat the procedure to find a first-order stationary point for the objective function. The size of the trust-region at each step is very critical to the effectiveness of the algorithm, particularly for large-scale problems, because minimizing the model at each step needs the gradient and the Hessian information of the objective function. Our modified trust-region algorithms are opportunistic in the sense that they explore beyond the trust-region if the boundary of the region prevents the algorithm from accepting a more beneficial point. It occurs when there is a very good agreement between the model and the objective function on the trust-region boundary, and we can find a step outside the trust-region with smaller value of the model while at which the agreement between the model and the objective function remains good. We show that the algorithms are convergent. Initial numerical experiments show that the proposed algorithms are more efficient than the traditional trust-region algorithm for a large majority of problems in the CUTEst suite.