Optimizing a 2D Function Satisfying Unimodality Properties

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.

• Type: Conference
• Year: 2005
• Where: ESA
• Authors: Erik D. Demaine, Stefan Langerman
• Keywords: Bivariate Function Varies, ESA 2005, Nontrivial Adversary Arguments, Nontrivial Optimization Algorithms