A General Iterative Procedure for Solving Nonsmooth Constrained Generalized Equations

Wei Ouyang () and Kui Mei
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Wei Ouyang: School of Mathematics, Yunnan Normal University, Kunming 650500, China
Kui Mei: School of Mathematics, Yunnan Normal University, Kunming 650500, China

Mathematics, 2023, vol. 11, issue 22, 1-17

Abstract: In this paper, we concentrate on an abstract iterative procedure for solving nonsmooth constrained generalized equations. This procedure employs both the property of weak point-based approximation and the approach of searching for a feasible inexact projection on the constrained set. Utilizing the contraction mapping principle, we establish higher order local convergence of the proposed method under the assumption of metric regularity property which ensures that the iterative procedure generates a sequence converging to a solution of the constrained generalized equation. Under strong metric regularity assumptions, we obtain that each sequence generated by this procedure converges to a solution. Furthermore, a restricted version of the proposed method is considered, for which we establish the desired convergence for each iterative sequence without a strong metric subregularity condition. The obtained results are new even for generalized equations without a constraint set.

Keywords: iterative sequence; constrained generalized equation; feasible inexact projection; metric regularity; point-based approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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