A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization

By Hongchao Zhang, William W. Hager. SIAM Journal on Optimization, 2004

663 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/1d7012dc7ea15593c4f78f31ca699f9b08e26673

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Yin Zhang
2. Chengbo Li
3. Zaiwen Wen
4. Wotao Yin
5. Natasa Krejic
6. Zhenghai Huang
7. Jein-Shan Chen
8. Shenglong Hu

In Numerical Analysis

1. Yin Zhang
2. Chengbo Li
3. Zaiwen Wen
4. Wotao Yin
5. Jein-Shan Chen
6. Shaohua Pan
7. Natasa Krejic
8. Zhenghai Huang

Citations in the corpus

• Convergence of a smoothing algorithm for symmetric cone complementarity problems with a nonmonotone line search (2009, methodology): “In Algorithm 3.3, a nonmonotone line search technique, introduced by Zhang and Hager [ 23 ] , is adopted.”
• A feasible method for optimization with orthogonality constraints (2012, methodology): “We adopt a nonmonotone line search method based on a strategy in [61].”
• Subsampled inexact Newton methods for minimizing large sums of convex functions (2018, background): “3 [32] Suppose that the assumptions A1 holds and x∗ is the unique minimizer of the function fN .”
• An efficient augmented Lagrangian method with applications to total variation minimization (2013, methodology): “3, we will extend the convergence proof in [40] to the case of minimizing the non-differentiable function ψ(x) defined in (5).”
• A Field Guide to Forward-Backward Splitting with a FASTA Implementation (2014, neutral): “eboulle for use with FISTA [42]. Many authors consider these line searches to be overly conservative, particularly for poorly conditioned problems [33], and prefer non-monotone line search conditions [46,47]. Rather than insisting upon an objective decrease on every iteration, non-monotone line sear”
• An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing (2010, methodology): “To validate the BB-like step, a nonmonotone line search algorithm (NLSA) advanced by Zhang and Hager [84] is integrated.”
• A Damped Gauss-Newton Method for the Second-Order Cone Complementarity Problem (2009, methodology): “We replaced the monotone line search of Algorithm 6.1 with a nonmonotone version as described by Zhang and Hager [25], i.e., we computed the smallest nonnegative integer l such that (ζ k + ρldk) ≤ Wk + σρl∇ (ζ k)T dk Table 1 Numerical results with Algorithm 6.1 and SeDuMi for the SOCPs Problem Dimen”