Convergence to a second-order critical point of composite nonsmooth problems by a trust region method

An algorithm for finding a first-order and second-order critical point of composite nonsmooth problems is proposed in this paper. For smooth problems, algorithms for searching such a point usually utilize the so called negative-curvature directions. In this paper, the method recently proposed for nonlinear semidefinite problems by the current author is extended for solving general … Read more

An Adaptive Trust-Region Method Without Function Evaluations

In this paper we propose an adaptive trust-region method for smooth unconstrained optimization. The update rule for the trust-region radius relies only on gradient evaluations. Assuming that the gradient of the objective function is Lipschitz continuous, we establish worst-case complexity bounds for the number of gradient evaluations required by the proposed method to generate approximate … Read more

A Trust Region Method for the Optimization of Noisy Functions

Classical trust region methods were designed to solve problems in which function and gradient information are exact. This paper considers the case when there are bounded errors (or noise) in the above computations and proposes a simple modification of the trust region method to cope with these errors. The new algorithm only requires information about … Read more