A class of gradient unconstrained minimization algorithms with adaptive stepsize

Modified Two-Point Stepsize Gradient Methods for Unconstrained Optimization

A Combined Variable Metric - Conjugate Gradient Algorithm for a Class of Large Scale Unconstrained Minimization Problems

An algorithm is being presented for a special class of unconstrained minimization problems. The algorithm exploits the special structure of the Hessian in the problems under consideration, It is based on applying Bertsekas' I-1] Scaled Partial Conjugate Gradient method with respect to a metric that is updated by the Rank One update, using gradients obtained in the preceeding steps. Two classes ...

Adaptive matrix algebras in unconstrained minimization

Article history: Received 8 August 2014 Accepted 9 January 2015 Available online 30 January 2015 Submitted by R. Brualdi MSC: 65K10 90C53 47J25

A new hybrid conjugate gradient algorithm for unconstrained optimization

In this paper, a new hybrid conjugate gradient algorithm is proposed for solving unconstrained optimization problems. This new method can generate sufficient descent directions unrelated to any line search. Moreover, the global convergence of the proposed method is proved under the Wolfe line search. Numerical experiments are also presented to show the efficiency of the proposed algorithm, espe...

New Sequential and Parallel Derivative-Free Algorithms for Unconstrained Minimization

This paper presents sequential and parallel derivative-free algorithms for finding a local minimum of smooth and nonsmooth functions of practical interest. It is proved that, under mild assumptions, a sufficient decrease condition holds for a nonsmooth function. Based on this property, the algorithms explore a set of search directions and move to a point with a sufficiently lower functional val...