On the finite convergence of a projected cutter method

TL;DR

This paper introduces a generalized projected cutter method for finding fixed points of cutters in convex analysis, extending previous approaches with broader assumptions and providing theoretical insights and comparisons.

Contribution

It presents a more general algorithm for fixed points of cutters with nonempty interior, expanding the theoretical framework beyond existing methods.

Findings

The method converges under broader parameter conditions.

Examples demonstrate the method's applicability and limitations.

Comparisons show improvements over classical approaches.

Abstract

The subgradient projection iteration is a classical method for solving a convex inequality. Motivated by works of Polyak and of Crombez, we present and analyze a more general method for finding a fixed point of a cutter, provided that the fixed point set has nonempty interior. Our assumptions on the parameters are more general than existing ones. Various limiting examples and comparisons are provided.