Optimizing a 2d function satisfying unimodality properties

Authors:
Erik D. Demaine;Stefan Langerman
Affiliations:
MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, MA;Département d’informatique, Université Libre de Bruxelles, ULB, Bruxelles, Belgium
Venue:
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Year:
2005

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Abstract

The number of probes needed by the best possible algorithm for locally or globally optimizing a bivariate function varies substantially depending on the assumptions made about the function. We consider a wide variety of assumptions—in particular, global unimodality, unimodality of rows and/or columns, and total unimodality—and prove tight or nearly tight upper and lower bounds in all cases. Our results include both nontrivial optimization algorithms and nontrivial adversary arguments depending on the scenario.