The velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared residuals. A finite element discretization of the functional is minimized by a trust-region method in which the trust-region radius is defined by a Sobolev norm and the trust-reg...

Line search method and trust region method are two important classes of techniques for solving optimization problems and have their advantages respectively. In this paper we use the Armijo line search rule in a more accurate way and propose a new line search method for unconstrained optimization problems. Global convergence and convergence rate of the new method are analyzed under mild conditio...

In this paper, we examine the sensitivity of trust-region algorithms on the parameters related to the step acceptance and update of the trust region. We show, in the context of unconstrained programming, that the numerical efficiency of these algorithms can easily be improved by choosing appropriate parameters. Recommended ranges of values for these parameters are exhibited on the basis of exte...

The recently proposed Riemannian Trust-Region method can be applied to the problem of computing extreme eigenpairs of a matrix pencil, with strong global convergence and local convergence properties. This paper addresses inherent inefficiencies of an explicit trustregion mechanism. We propose a new algorithm, the Implicit Riemannian Trust-Region method for extreme eigenpair computation, which s...

In this paper we develop a trust region algorithm for constrained parabolic boundary control problems. The method is a projected form of the Steihaug trust-region-CG method with a smoothing step added at each iteration to improve performance in the global phase and provide mesh-independent sup-norm convergence in the terminal phase.

We propose a new and efficient nonmonotone adaptive trust region algorithm to solve unconstrained optimization problems. This incorporates two novelties: it benefits from radius dependent shrinkage parameter for adjusting the that avoids undesirable directions exploits strategy prevent sudden increments of objective function values in techniques. Global convergence this is investigated under so...

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 large amount of on-policy interaction with the environment. To address this problem, we propose an off-policy trust region method, Trust-PCL, which exploits an observati...

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 large amount of on-policy interaction with the environment. To address this problem, we propose an off-policy trust region method, Trust-PCL, which exploits an observati...