Open AccessSolution method for discrete double obstacle problems based on a power penalty approach
Author(s) -
Kai Zhang,
Xiaohui Yang,
Song Wang
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2021018
Subject(s) - penalty method , obstacle , obstacle problem , mathematics , power (physics) , nonlinear system , exponential function , mathematical optimization , computer science , mathematical analysis , physics , variational inequality , law , quantum mechanics , political science
We develop a power penalty approach to a finite-dimensional double obstacle problem. This problem is first approximated by a system of nonlinear equations containing two penalty terms. We show that the solution to this penalized equation converges to that of the original obstacle problem at an exponential rate when the coefficient matrices are \begin{document}$ M $\end{document} -matrices. Numerical examples are presented to confirm the theoretical findings and illustrate the efficiency and effectiveness of the new method.