Convex version of multivariate adaptive regression splines for optimization

Thomas D. Shih, Victoria C P Chen, Seoung Bum Kim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Multivariate Adpative Regression Splines (MARS) provide a flexible statistical modeling method that employs forward and backward search algorithms to identify the combination of basis functions that best fits the data. In optimization, MARS has been used successfully to estimate the value function in stochastic dynamic programming, and MARS could be potentially useful in many real world optimization problems where objective (or other) functions need to be estimated from data, such as in simulation optimization. Many optimization methods depend on convexity, but a nonconvex MARS approximation is inherently possible because interaction terms are products of univariate terms. In this paper, we propose a convex version of MARS. In order to ensure MARS convexity, two major modifications are made: (1) coefficients are constrained such that pairs of basis functions are guaranteed to jointly form convex functions; (2) The form of interaction terms is appropriately changed. Finally, MARS convexity can be achieved by the fact that the sum of convex functions is convex.

Original languageEnglish
Title of host publication2006 IIE Annual Conference and Exhibition
Publication statusPublished - 2006 Dec 1
Externally publishedYes
Event2006 IIE Annual Conference and Exposition - Orlando, FL, United States
Duration: 2006 May 202006 May 24

Other

Other2006 IIE Annual Conference and Exposition
CountryUnited States
CityOrlando, FL
Period06/5/2006/5/24

    Fingerprint

Keywords

  • Convexity
  • Function approximation
  • Optimization
  • Regression splines

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering

Cite this

Shih, T. D., Chen, V. C. P., & Kim, S. B. (2006). Convex version of multivariate adaptive regression splines for optimization. In 2006 IIE Annual Conference and Exhibition