Optimizing a 2D function satisfying unimodality properties

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. © Springer-Verlag Berlin Heidelberg 2005.