BFGS convergence to nonsmooth minimizers of convex functions

2017/03/20 by Jiayi Guo, Guo, Jiayi, Adrian S. Lewis +1
Computer Science · Engineering · Mathematics · #65K05 #90C30 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1703.06690

openalex publication_date 2017/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The popular BFGS quasi-Newton minimization algorithm under reasonable conditions converges globally on smooth convex functions. This result was proved by Powell in 1976: we consider its implications for functions that are not smooth. In particular, an analogous convergence result holds for functions, like the Euclidean norm, that are nonsmooth at the minimizer.

Citations

• Geometric categories and o-minimal structures
• Numerical optimization

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