In this paper, we present a nonmonotone trust-region method of conic model for unconstrained optimization. The new method combines a new trust-region subproblem of conic model proposed in [Y. Ji, S.J. Qu, Y.J. Wang, H.M. Li, A conic trust-region method for optimization with nonlinear equality and inequality 4 constrains via active-set strategy, Appl. Math. Comput. 183 (2006) 217–231] with a non...

Trust is a critical social process that helps us to cooperate with others and is present to some degree in all human interaction. However, the underlying brain mechanisms of conditional and unconditional trust in social reciprocal exchange are still obscure. Here, we used hyperfunctional magnetic resonance imaging, in which two strangers interacted online with one another in a sequential recipr...

In this paper we study the global convergence behavior of a class of composite–step trust–region SQP methods that allow inexact problem information. The inexact problem information can result from iterative linear systems solves within the trust–region SQP method or from approximations of first–order derivatives. Accuracy requirements in our trust– region SQP methods are adjusted based on feasi...

In this paper, we present a nonmonotone trust-region algorithm for unconstrained optimization. We first introduce a variant of the nonmonotone strategy proposed by Ahookhosh and Amini cite{AhA 01} and incorporate it into the trust-region framework to construct a more efficient approach. Our new nonmonotone strategy combines the current function value with the maximum function values in some pri...

A line-search method, based on retractions, is formulated on Riemannian manifolds. This Riemannian line-search method, as well as a previouslyproposed Riemannian trust-region method, are further generalized to accelerated line-search and trust-region methods, where the next iterate is allowed to be any point that produces at least as much decrease in the cost function as a fixed fraction of the...

Model-free reinforcement learning (RL) methods are succeeding in a growing number of tasks, aided by recent advances in deep learning. They tend to suffer from high sample complexity, however, 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...

Model-free reinforcement learning (RL) methods are succeeding in a growing number of tasks, aided by recent advances in deep learning. They tend to suffer from high sample complexity, however, 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...

The so-called Trust-Region Subproblem gets its name in the trust-region method in optimization and also plays a vital role in various other applications. Several numerical algorithms have been proposed in the literature for solving small-to-medium size dense problems as well as for large scale sparse problems. The Generalized Lanczos Trust-Region (GLTR) method proposed by [Gould, Lucidi, Roma a...

In this article, we consider solvers for large-scale trust-region subproblems when the quadratic model is defined by a limited-memory symmetric rank-one (L-SR1) quasi-Newton matrix. We propose a solver that exploits the compact representation of L-SR1 matrices. Our approach makes use of both an orthonormal basis for the eigenspace of the L-SR1 matrix and the ShermanMorrison-Woodbury formula to ...

Bilevel programs form a class of hierarchical optimzation problems in which the constraint set is not explicit but is defined in terms of another optimization problem. Optimization problems in several real-life domains can be expressed as bilevel programs, making such problems ubiquitous. In this term paper, we analyze a trust region approach for solving a special case of this problem.