Inverse problems for multi-valued quasi variational inequalities and noncoercive variational inequalities with noisy data. (3rd October 2019)

• Record Type: Journal Article
• Authors: Khan, Akhtar A.; Migorski, Stanislaw; Sama, Miguel
• Is Part Of: Optimization. Volume 68:Number 10(2019)
• Page Start: 1897
• Page End: 1931
• Publication Date: 2019-10-03
• Subjects: Inverse problems -- variational inequalities -- quasi-variational inequalities -- regularization; 35R30 -- 49N45 -- 65J20 -- 65J22 -- 65M30; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1604706
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: We study the inverse problem of identifying a variable parameter in variational and quasi-variational inequalities. We consider a quasi-variational inequality involving a multi-valued monotone map and give a new existence result. We then formulate the inverse problem as an optimization problem and prove its solvability. We also conduct a thorough study of the inverse problem of parameter identification in noncoercive variational inequalities which appear commonly in applied models. We study the inverse problem by posing optimization problems using the output least-squares and the modified output least-squares. Using regularization, penalization, and smoothing, we obtain a single-valued parameter-to-selection map and study its differentiability. We consider optimization problems using the output least-squares and the modified output least-squares for the regularized, penalized and smoothened variational inequality. We give existence results, convergence analysis, and optimality conditions. We provide applications and numerical examples to justify the proposed framework.