A new nonmonotone line search technique for unconstrained optimization

Abstract

In this paper, we propose a new nonmonotone line search technique for unconstrained optimization problems. By using this new technique, we establish the global convergence under conditions weaker than those of the existed nonmonotone line search techniques.

A Nonmonotone Line Search Slackness Technique for Unconstrained Optimization

“…2, we slacken the nonmonotone F-rule of Sun et al [3] and introduce the nonmonotone slackness rule. The convergence of the line search algorithm based on the new rule is confirmed by virtue of [3] and [4] in Sect. 3.…”

“…However, subsequent studies showed that the convergence rate of monotone line search technique may reduce considerably when the iteration locates in a narrow curved valley. See [2][3][4] for details.…”

“…Then, this rule was improved by [4] in 2008. The nonmonotone F-rule and its improved version are effective in practice for many situations.…”

“…Recent studies [2][3][4] indicate that monotone line search rules converge very slowly when the iteration points locate near a valley bottom. To overcome this problem, Grippo et al [2] introduced the idea of nonmonotone line search, and their numerical tests illustrate its effectiveness.…”

Nonmonotone hybrid tabu search for inequalities and equalities: an experimental study

“…This is important since, far from the solution, the likelihood of detecting a global solution instead of a local one is high when the merit function has a sufficient decrease, relative to the maximum merit values of previous iterations, of more than a certain quantity,η k . Similar nonmonotone F-rules for line search with guaranteed convergence in optimization context are available in the literature [37,41]. In [40], a nonmonotone trust region procedure using a filter methodology to handle the equality constraints of an optimization problem is presented.…”