SIAM Journal on Optimization· 2013Q1
A Nonlinear Conjugate Gradient Algorithm with an Optimal Property and an Improved Wolfe Line Search
- 306citations
- Q1SCImago
- 2013year
Short summary
A new family of conjugate gradient methods for unconstrained optimization is proposed, featuring a direction closest to the scaled memoryless BFGS method and an improved Wolfe line search that avoids numerical drawbacks and ensures global convergence.
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Key points
- Proposes a family of conjugate gradient methods for unconstrained optimization.
- Introduces an improved Wolfe line search to avoid numerical drawbacks and ensure global convergence.
- Incorporates adaptive restarts along negative gradients to accelerate the algorithm.
- Numerical experiments on the CUTEr collection indicate promising performance.
AI-generated from the title and abstract; the full text is not read.
Abstract
In this paper, we seek the conjugate gradient direction closest to the direction of the scaled memoryless BFGS method and propose a family of conjugate gradient methods for unconstrained optimization. An improved Wolfe line search is also proposed, which can avoid a numerical drawback of the original Wolfe line search and guarantee the global convergence of the conjugate gradient method under mild conditions. To accelerate the algorithm, we introduce adaptive restarts along negative gradients based on the extent to which the function approximates some quadratic function during previous iterations. Numerical experiments with the CUTEr collection show that the proposed algorithm is promising.
The authors' abstract, as published at the source. SIAM Journal on Optimization, 2013 · DOI ↗
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Field: Numerical Analysis
Numerical AnalysisMathematics