Convergence Of Trust Region Method Research Articles

An accelerated nonmonotone trust region method with adaptive trust region for unconstrained optimization

Trust region method is a robust method for optimization problems. In this paper, we propose a novel adaptive nonmonotone technique based on trust region methods for solving unconstrained optimization. In order to accelerate the convergence of trust region methods, an adaptive trust region is generated according to the Hessian of the iterate point. Both the nonmonotone techniques and this adaptive strategies can improve the trust region methods in the sense of convergence. We prove that the proposed method is locally superlinear convergence under some standard assumptions. Numerical results show that the new method is effective and has a high speed of convergence in practice.

A Trust Region Algorithm Using Curve-Linear Searching Direction for Unconstrained Optimization

In the paper, aimed at the shortcoming of trust region method, we proposed a algorithm using negative curvature direction as its searching direction. The convergence of the algorithm was given. Furthermore, combing trust region method and curve-linear searching techniques, a trust region algorithm, using general curve-linear searching direction, was proposed. We proved its efficiency and feasibility. The algorithm has adjustability and can select or update its searching direction according to the iteration. This allows the algorithm that has the properties of curve-linear searching method and the global convergence of trust region method. Finally, we indicate that some searching directions of common methods can be as a special searching direction of the general method.

A unified approach to global convergence of trust region methods for nonsmooth optimization

This paper investigates the global convergence of trust region (TR) methods for solving nonsmooth minimization problems. For a class of nonsmooth objective functions called regular functions, conditions are found on the TR local models that imply three fundamental convergence properties. These conditions are shown to be satisfied by appropriate forms of Fletcher's TR method for solving constrained optimization problems, Powell and Yuan's TR method for solving nonlinear fitting problems, Zhang, Kim and Lasdon's successive linear programming method for solving constrained problems, Duff, Nocedal and Reid's TR method for solving systems of nonlinear equations, and El Hallabi and Tapia's TR method for solving systems of nonlinear equations. Thus our results can be viewed as a unified convergence theory for TR methods for nonsmooth problems.