Abstract
In this work, we present a novel power penalty method for the approximation of a global solution to a double obstacle complementarity problem involving a semilinear parabolic differential operator and a bounded feasible solution set. We first rewrite the double obstacle complementarity problem as a double obstacle variational inequality problem. Then, we construct a semilinear parabolic partial differential equation (penalized equation) for approximating the variational inequality problem. We prove that the solution to the penalized equation converges to that of the variational inequality problem and obtain a convergence rate that is corresponding to the power used in the formulation of the penalized equation. Numerical results are presented to demonstrate the theoretical findings.
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The authors are grateful to the referees and Associate Editor for their valuable comments and constructive suggestions for improving the paper.
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This research was supported by Grants from Natural Science Foundation of China (11071180), ( 11171247), (10831009), The Hong Kong Polytechnic University (G-YX1Q) and the Research Grants Council of Hong Kong (PolyU 5306/11E).
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Zhou, Y.Y., Wang, S. & Yang, X.Q. A penalty approximation method for a semilinear parabolic double obstacle problem. J Glob Optim 60, 531–550 (2014). https://doi.org/10.1007/s10898-013-0122-6
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DOI: https://doi.org/10.1007/s10898-013-0122-6
Keywords
- Parabolic differential operator
- Complementarity problem
- Global optimizer
- Penalty approximation method
- Double obstacle problem