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AN INEXACT UZAWA ALGORITHMIC FRAMEWORK FOR NONLINEAR SADDLE POINT PROBLEMS WITH APPLICATIONS TO ELLIPTIC OPTIMAL CONTROL PROBLEM

Song Y (2019)

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Publication Language: English

Publication Status: Published

Publication Type: Journal article

Publication year: 2019

Journal

Publisher: SIAM PUBLICATIONS

Book Volume: 57

Pages Range: 2656-2684

Journal Issue: 6

DOI: 10.1137/19M1245736

Abstract

We consider a class of nonlinear saddle point problems with various applications in PDEs and optimal control problems and propose an algorithmic framework based on some inexact Uzawa methods in the literature. Under mild conditions, the convergence of this algorithmic framework is uniformly proved and the linear convergence rate is estimated. We take an elliptic optimal control problem with control constraints as an example to illustrate how to choose application-tailored preconditioners to generate specific and efficient algorithms by the algorithmic framework. The resulting algorithm does not need to solve any optimization subproblems or systems of linear equations in its iteration; each of its iterations only requires the projection onto a simple admissible set, four algebraic multigrid V-cycles, and a few matrix-vector multiplications. Its numerical efficiency is then demonstrated by some preliminary numerical results.

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How to cite

APA:

Song, Y. (2019). AN INEXACT UZAWA ALGORITHMIC FRAMEWORK FOR NONLINEAR SADDLE POINT PROBLEMS WITH APPLICATIONS TO ELLIPTIC OPTIMAL CONTROL PROBLEM. SIAM Journal on Numerical Analysis, 57(6), 2656-2684. https://dx.doi.org/10.1137/19M1245736

MLA:

Song, Yongcun. "AN INEXACT UZAWA ALGORITHMIC FRAMEWORK FOR NONLINEAR SADDLE POINT PROBLEMS WITH APPLICATIONS TO ELLIPTIC OPTIMAL CONTROL PROBLEM." SIAM Journal on Numerical Analysis 57.6 (2019): 2656-2684.

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