This work presents a global convergence theory for a broad class of trust-region algorithms for the smooth nonlinear programming problem with equality constraints. The main result generalizes Powell's 1975 result for unconstrained trust-region algorithms. The trial step is characterized by very mild conditions on its normal and tangential components. The normal component need not be computed ac...

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...

A general scheme for trust-region methods on Riemannian manifolds is proposed. A truncated conjugate-gradient method is utilized to solve the trust-region subproblems. The method is illustrated several problems of numerical linear algebra.

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 curvelinear searching direction, was proposed. We proved its efficiency and feasibi...

In this paper we run two important methods for solving some well-known problems and make a comparison on their performance and efficiency in solving nonlinear systems of equations‎. ‎One of these methods is a non-monotone adaptive trust region strategy and another one is a scaled trust region approach‎. ‎Each of methods showed fast convergence in special problems and slow convergence in other o...

We consider the problem of finding an approximate minimizer of a general quadratic function subject to a two-norm constraint. The Steihaug-Toint method minimizes the quadratic over a sequence of expanding subspaces until the iterates either converge to an interior point or cross the constraint boundary. The benefit of this approach is that an approximate solution may be obtained with minimal wo...

In this paper W E present a method for robustly and accurately estimating the rotation and translation between a camera and a 3-D object f r o m point and line correspondences. First we devise an error function and second we show how to minimize this error function. The quadratic nature of this function is made possible by representing rotation and translation with a dual number quaternion. W e...

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...