Journal of Optimization Theory and Applications

, Volume 153, Issue 3, pp 633–649

Hull-Volume with Applications to Convergence Analysis

Article

DOI: 10.1007/s10957-011-9959-3

Cite this article as:
Levy, A.B. J Optim Theory Appl (2012) 153: 633. doi:10.1007/s10957-011-9959-3

Abstract

We introduce and study decompositions of finite sets as well as coverings of their convex hulls, and use these objects to develop various estimates of and formulas for the “hull-volume” of the sets (i.e., the volume of their convex hull). We apply our results to the convergence analysis of the “iterate-sets” associated with each iteration of a reduce-or-retreat optimization method (including pattern-search methods like Nelder–Mead as well as model-based methods).

Keywords

PolytopeConvex hullSimplexVolumeNumerical optimizationConvergence analysis

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsBowdoin CollegeBrunswickUSA