Many large-scale finite-dimensional optimization problems arise from the discretization of infinite-dimensional problems, a primary example being optimal-control problems defined in terms of either ordinary or partial differential equations. While the direct solution of such problems for a discretization level yielding the desired accuracy is often possible using existing packages for large-sca...

In this paper we address the problem of tracking a human being using an optimization method. In particular, our task is to use a trust-region approach for optimization and to overcome the occlusion problem. We present the development of an algorithm to track the target as well as a description of the problems encountered while implementing the algorithm in Matlab. As a result, we evaluate infor...

We present a new method for regularization of ill-conditioned problems, such as those that arise in image restoration or mathematical processing of medical data. The method extends the traditional trust-region subproblem, TRS, approach that makes use of the L-curve maximum curvature criterion, a strategy recently proposed to find a good regularization parameter. We apply a parameterized trust r...

Normalized Cuts has successfully been applied to a wide range of tasks in computer vision, it is indisputably one of the most popular segmentation algorithms in use today. A number of extensions to this approach have also been proposed, ones that can deal with multiple classes or that can incorporate a priori information in the form of grouping constraints. It was recently shown how a general l...

Unconstrained optimization problems are closely related to systems of ordinary differential equations (ODEs) with gradient structure. In this work, we prove results that apply to both areas. We analyze the convergence properties of a trust region, or Levenberg–Marquardt, algorithm for optimization. The algorithm may also be regarded as a linearized implicit Euler method with adaptive timestep f...

A general scheme for trust-region methods on Riemannian manifolds is proposed and analyzed. Among the various approaches available to (approximately) solve the trust-region subproblems, particular attention is paid to the truncated conjugate-gradient technique. The method is illustrated on problems from numerical linear algebra.

This document is an expanded version of [ABG05], with a detailed convergence analysis. A general scheme for trust-region methods on Riemannian manifolds is proposed and analyzed. Among the various approaches available to (approximately) solve the trust-region subproblems, particular attention is paid to the truncated conjugate-gradient technique. The method is illustrated on problems from numer...

We propose an algorithm for nonlinear optimization that employs both trust region techniques and line searches Unlike traditional trust region methods our algorithm does not resolve the subproblem if the trial step results in an increase in the objective function but instead performs a backtracking line search from the failed point Backtracking can be done along a straight line or along a curve...

Protein alignment is a challenging applied optimization problem. Superposition methods are based on the maximization of a score function with respect to rigid-body modifications of relative positions. The problem of score maximization can be modelled as a continuous nonsmooth optimization problem (low order-value optimization (LOVO)). This allows one to define practical and convergent methods t...

Global convergence to rst-order critical points is proved for two trust-region SQP-lter algorithms of the type introduced by Fletcher and Leyyer (1997). The algorithms allow for an approximate solution of the quadratic subproblem and incorporate the safeguarding tests described in Fletcher, Leyyer and Toint (1998). The rst algorithm decomposes the step into its normal and tangential components ...