The goal of this paper is to show that the use of minimum Frobenius norm quadratic models can improve the performance of direct-search methods. The approach taken here is to maintain the structure of directional direct-search methods, organized around a search and a poll step, and to use the set of previously evaluated points generated during a direct-search run to build the models. The minimiz...

Trust region methods, such as TRPO, are often used to stabilize policy optimization algorithms in reinforcement learning (RL). While current trust region strategies are effective for continuous control, they typically require a prohibitively large amount of on-policy interaction with the environment. To address this problem, we propose an offpolicy trust region method, Trust-PCL. The algorithm ...

The classical trust-region method for unconstrained minimization can be augmented with a line search that finds a point that satisfies the Wolfe conditions. One can use this new method to define an algorithm that simultaneously satisfies the quasi-Newton condition at each iteration and maintains a positive-definite approximation to the Hessian of the objective function. This new algorithm has s...

In this paper, we review the trust region algorithms for nonlinear optimization. The philosophy and the fundamental ideas of trust region algorithms are discussed. Model algorithms for unconstrained optimization, constrained optimization, and nonsmooth optimization are given. Main techniques for global convergence and local superlinear convergence are analyzed.

The interval bounded generalized trust region subproblem (GTRS) consists in minimizing a general quadratic objective, q0(x) → min, subject to an upper and lower bounded general quadratic constraint, l ≤ q1(x) ≤ u. This means that there are no definiteness assumptions on either quadratic function. We first study characterizations of optimality for this implicitly convex problem under a constrain...

We describe a MATLAB implementation [6] of the method LSTRS [5] for the large-scale trust-region subproblem:

This paper develops a formal model of topological relations between a directed line segment (DLine) and a region in a two-dimensional space. Such model forms a foundation for characterizing movement patterns of an agent with respect to a region. The DLine-region relations are captured by the 9intersection for line-region relations with further distinction of the line’s boundary into two subpart...

In this paper we investigate the numerical performance of trust-region algorithms in which the trust-region radius is updated by a nonlinear rule according with the quality of the models. This class of algorithms fits into the Nonlinear Stepsize Control framework recently proposed by Toint (Optimization Methods and Software 28: 82–95, 2013). The nonlinear control of the trust-region radius is c...

The classical trust region algorithm was extended to the nonsmooth minimization problem successful by Qi and Sun. Combining the trust region algorithm of Qi and Sun and the trust region algorithm with radius bounded below of Jiang for solving generalized complementarity problems, this paper present a new trust region algorithm with radius bounded below for the unconstrained nonsmooth optimizati...