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This research aims to improve the efficiency of solving nonlinear composite optimization problems using adaptive Barzilai-Borwein methods.

June 3, 2026Numerical AlgorithmsOpen Access

Adaptive proximal Barzilai-Borwein methods for nonlinear composite optimization

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Randomized trial demonstrates enhanced convergence in nonlinear composite optimization using adaptive stepsizes, suggesting improved efficiency.

This research aims to improve the efficiency of solving nonlinear composite optimization problems using adaptive Barzilai-Borwein methods.
Introduced adaptive stepsize rules for convex functions eliminating line searches
Developed a nonmonotone line search strategy for nonconvex functions
Conducted extensive numerical experiments to compare proposed methods with existing techniques.
Achieved global convergence for both convex and nonconvex cases under specified conditions
Proposed methods outperformed existing proximal gradient methods in numerical tests
Convergence rates were analyzed and supported through experiments.

Pandey et al. (2026) studied this question.

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Randomized trial demonstrates enhanced convergence in nonlinear composite optimization using adaptive stepsizes, suggesting improved efficiency.