We solve the non-linearized and linearized obstacle problems efficiently using a primal-dual hybrid gradients method involving projection and/or ?1 penalty. Since this method requires no matrix inversions or explicit identification of the contact set, we find that this method, on a variety of test problems, achieves the precision of previous methods with a speed up of 1–2 orders of magnitude. The derivation of this method is disciplined, relying on a saddle point formulation of the convex problem, and can be adapted to a wide range of other constrained convex optimization problems.
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Zosso, D., Osting, B., Xia, M., and Osher, S., "An Efficient Primal-Dual Method for the Obstacle Problem", J Sci Comput (2017) 73(1):416-437.
Dominique Zosso (2020). Efficient Primal-Dual Method for the Obstacle Problem (https://www.mathworks.com/matlabcentral/fileexchange/71886-efficient-primal-dual-method-for-the-obstacle-problem), MATLAB Central File Exchange. Retrieved .
Zosso, Dominique, et al. “An Efficient Primal-Dual Method for the Obstacle Problem.” Journal of Scientific Computing, vol. 73, no. 1, Springer Nature, Mar. 2017, pp. 416–37, doi:10.1007/s10915-017-0420-0.
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