On efficiency of nonmonotone Armijo-type line searches

•A comprehensive introduction about nonmonotone methods is provided.•Two novel nonmonotone terms and related convergence analysis are given.•Numerical results show the efficiency of state-of-the-art nonmonotone methods. Monotonicity and nonmonotonicity play a key role in studying the global converge...

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Bibliographic Details
Published in:Applied Mathematical Modelling 2017-03, Vol.43, p.170-190
Main Authors: Ahookhosh, Masoud, Ghaderi, Susan
Format: Article
Language:English
Subjects:
Armijo-type line search
Computational efficiency
Convergence
Efficiency
First- and second-order black-box information
Global convergence
Iterative methods
Nonlinear programming
Nonmonotone strategy
Optimization
Searching
Studies
Unconstrained optimization
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Summary:•A comprehensive introduction about nonmonotone methods is provided.•Two novel nonmonotone terms and related convergence analysis are given.•Numerical results show the efficiency of state-of-the-art nonmonotone methods. Monotonicity and nonmonotonicity play a key role in studying the global convergence and the efficiency of iterative schemes employed in the field of nonlinear optimization, where globally convergent and computationally efficient schemes are explored. This paper addresses some features of descent schemes and the motivation behind nonmonotone strategies and investigates the efficiency of an Armijo-type line search equipped with some popular nonmonotone terms. More specifically, we propose two novel nonmonotone terms, combine them into Armijo’s rule and establish the global convergence of sequences generated by these schemes. Furthermore, we report extensive numerical results and comparisons indicating the performance of the nonmonotone Armijo-type line searches using the most popular search directions on the CUTEst test collection of unconstrained problems. We finally apply the considered nonmonotone schemes to a deblurring problem to recover a blurred/noisy image.
ISSN:0307-904X
1088-8691
0307-904X
DOI:10.1016/j.apm.2016.10.055