DOI: 10.24193/fpt-ro.2025.2.10

Authors: Yunshu Fu and Hong-Kun Xu

Abstract: Subgradient methods, introduced by Shor and developed by Albert, Iusem, Nesterov, Polyak, Solodov, and many others, are used to solve nondifferentiable optimization problems. In this paper we discuss weak and strong convergence of projected subgradient methods in an infinite-dimensional Hilbert space. We apply the viscosity approximation method to the projected subgradient method to obtain strongly convergent subgradient algorithms. In addition, we develop the forcing strong convergence technique and the CQ algorithm to solve nondifferentiable convex optimization problems.

Key Words and Phrases: Projection, ε-subgradient, nondifferentiable convex optimization, variational inequality, strong convergence, infinite-dimensional.

2010 Mathematics Subject Classification: 90C25, 47J25, 47H26, 47H10.

Published on-line: May 1st, 2025.

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