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This is a Quantitative Study study.

October 16, 2025Open Access

A Non-Monotone Line-Search Method for Minimizing Functions with Spurious Local Minima

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A new method improves performance in minimizing objective functions with multiple local minima, suggesting efficiency in optimization.

New non-monotone line-search method effectively minimizes functions with spurious local minima, enhancing escape from local solutions.
The method utilizes a relaxed Armijo condition, allowing controlled increases in function values between iterations.
Worst-case complexity estimates show its effectiveness for functions with Lipschitz continuous gradients in reaching approximate stationary points.
Numerical results highlight its significant performance advantage over existing non-monotone methods in handling local minima.

Aminifard et al. (2025) studied this question.

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