1 research outputs found
Adaptive Interpolation Strategies in Derivative-Free Optimization: a case study
Derivative-Free optimization (DFO) focuses on designing methods to solve
optimization problems without the analytical knowledge of gradients of the
objective function. There are two main families of DFO methods: model-based
methods and direct search methods. In model-based DFO methods, a model of the
objective function is constructed using only objective function values, and the
model is used to guide the computation of the next iterate. Natural questions
in this class of algorithms include how many function evaluations should be
used to construct the model? And, should this number be fixed, or adaptively
selected by the algorithm? In this paper, we numerically examine these
questions, using Hare and Lucet's Derivative-Free Proximal Point (DFPP)
algorithm [Hare, Lucet, 2014] as a case study. Results suggest that the number
of function evaluations used to construct the model has a huge impact on
algorithm performance, and adaptive strategies can both improve and hinder
algorithm performance