Error bound conditions and convergence of optimization methods on smooth\n and proximally smooth manifolds

2019/12/10 by M. V. Balashov, Balashov, Maxim, Andrey Tremba +1 · 1 citation
Computer Science · Engineering · Mathematics · #46N10 #65K05 #65K10 #90C26 #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.1912.04660

openalex publication_date 2019/12/10 · openalex created_date 2022/07/23 · openalex updated_date 2026/07/28

Abstract

We analyse the convergence of the gradient projection algorithm, which is\nfinalized with the Newton method, to a stationary point for the problem of\nnonconvex constrained optimization \min_{x \∈ S} f(x) with a proximally\nsmooth set S = x \∈ Rⁿ : g(x) = 0 , ; g : Rⁿ \→ R^m and a\nsmooth function f. We propose new Error bound (EB) conditions for the\ngradient projection method which lead to the convergence domain of the Newton\nmethod. We prove that these EB conditions are typical for a wide class of\noptimization problems. It is possible to reach high convergence rate of the\nalgorithm by switching to the Newton method.\n

Cited by

• Quantitative Convergence Analysis of Projected Stochastic Gradient Descent for Non-Convex Losses via the Goldstein Subdifferential

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