Continuous local search
Author(s)
Daskalakis, Constantinos; Papadimitriou, Christos
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We introduce CLS, for continuous local search, a class of polynomial-time checkable total functions that lies at the intersection of PPAD and PLS, and captures a particularly benign kind of local optimization in which the domain is continuous, as opposed to combinatorial, and the functions involved are continuous. We show that this class contains several well known intriguing problems which were heretofore known to lie in the intersection of PLS and PPAD but were otherwise unclassifiable: Finding fixpoints of contraction maps, the linear complementarity problem for P matrices, finding a stationary point of a low-degree polynomial objective, the simple stochastic games of Shapley and Condon, and finding a mixed Nash equilibrium in congestion, implicit congestion, and network coordination games. The last four problems belong to CCLS, for convex CLS, another subclass of PPAD ∩ PLS seeking the componentwise local minimum of a componentwise convex function. It is open whether any or all of these problems are complete for the corresponding classes.
Date issued
2011-01Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer ScienceJournal
Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '11)
Publisher
Society for Industrial and Applied Mathematics
Citation
Constantinos Daskalakis and Christos Papadimitriou. "Continuous local search." In Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '11). SIAM 790-804. SIAM ©2011
Version: Final published version