Model-free reinforcement learning (RL) methods are succeeding in a growing number of tasks, aided by recent advances in deep learning. However, they tend to suffer from high sample complexity which hinders their use in real-world domains. Alternatively, model-based reinforcement learning promises to reduce sample complexity, but tends to require careful tuning and to date have succeeded mainly ...

We consider the global minimization of a bound-constrained function with a so-called funnel structure. We develop a two-phase procedure that uses sampling, local optimization, and Gaussian smoothing to construct a smooth model of the underlying funnel. The procedure is embedded in a trust-region framework that avoids the pitfalls of a fixed sampling radius. We present a numerical comparison to ...

An algorithm for smooth nonlinear constrained optimization problems is described, in which a sequence of feasible iterates is generated by solving a trust-region sequential quadratic programming (SQP) subproblem at each iteration, and perturbing the resulting step to retain feasibility of each iterate. By retaining feasibility, the algorithm avoids several complications of other trust-region SQ...

We introduce a trust region algorithm for minimization of nons-mooth functions with linear constraints. At each iteration, the objective function is approximated by a model fuction that satisses a set of assumptions stated recently by Qi and Sun in the context of unconstrained nonsmooth optimization. The trust region iteration begins with the resolution of an \easy problem", as in recent works ...

Trust-region methods for solving large bound-constrained nonlinear systems are considered. These allow for spherical or elliptical trust-regions where the search for an approximate solution is restricted to a low dimensional space. A general formulation for these methods is introduced and global and superlinear/quadratic convergence is shown under standard assumptions. Viable approaches for imp...

We study large scale extended trust region subproblems (eTRS) i.e., the minimization of a general quadratic function subject to a norm constraint, known as the trust region subproblem (TRS) but with an additional linear inequality constraint. It is well known that strong duality holds for the TRS and that there are efficient algorithms for solving large scale TRS problems. It is also known that...

In this paper we solve large scale ill-posed problems, particularly the image restoration problem in atmospheric imaging sciences, by a trust region-CG algorithm. Image restoration involves the removal or minimization of degradation (blur, clutter, noise, etc.) in an image using a priori knowledge about the degradation phenomena. Our basic technique is the so-called trust region method, while t...

We consider the numerical treatment of the optical flow problem by evaluating the performance of the trust region method versus the line search method. To the best of our knowledge, the trust region method is studied here for the first time for variational optical flow computation. Four different optical flow models are used to test the performance of the proposed algorithm combining linear and...

Given a function f0 defined on the unit square Ω with values in R, we construct a piecewise linear function f on a triangulation of Ω such that f agrees with f0 on the boundary nodes, and the image of f has minimal surface area. The problem is formulated as that of minimizing a discretization of a least squares functional whose critical points are uniformly parameterized minimal surfaces. The n...

Trust region method for a class of large-scale minimization problems, the unconstrained discrete-time optimal control (DTOC) problems, is considered. Although the trust region algorithms developed in 4] and 13] are very economical they lack the ability to handle the so-called hard case. In this paper, We show that the trust region subproblem can be solved within an acceptable accuracy without f...