A General Iterative Procedure to Solve Generalized Equations with Differentiable Multifunction

Gaydu, Michaël; Silva, Gilson N.

doi:10.1007/s10957-020-01635-8

Cited by 4 publications

(2 citation statements)

References 23 publications

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“…For n = α = 0, one needs to make κ, τ, and η sufficiently small to ensure the validity of ( 15) and (25), and in this case we have linear convergence.…”

Section: Remarkmentioning

confidence: 99%

“…Geoffroy and Piétrus proposed in [24] a generalized concept of point-based approximation to generate an iterative procedure for generalized equations. The authors obtained convergence results on the nonsmooth Newton-type procedure which includes both local and semilocal versions (see [12,13,16,[24][25][26] and the references therein). Inexact Newton methods for solving smooth equation f (x) = 0 in finite dimensions (i.e., (1) with F ≡ 0 and X = Y = R n ) were introduced by Dembo, Eisenstat, and Steihaug [27].…”

Section: Introductionmentioning

confidence: 99%

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A General Iterative Procedure for Solving Nonsmooth Constrained Generalized Equations

Ouyang,

Mei

2023

Mathematics

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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.

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“…For n = α = 0, one needs to make κ, τ, and η sufficiently small to ensure the validity of ( 15) and (25), and in this case we have linear convergence.…”

Section: Remarkmentioning

confidence: 99%