Convex Versions Of Multivariate Adaptive Regression Splines And Implementations For Complex Optimization Problems

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Title: Convex Versions Of Multivariate Adaptive Regression Splines And Implementations For Complex Optimization Problems
Author: Shih, Dachuan Thomas
Abstract: Multivariate Adaptive 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 dissertation , convex versions of MARS are proposed . 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 . The implementation of MARS for approximating complex optimization functions can involve hundreds to thousands of state or decision variables . In particular , this research studies application to an inventory forecasting stochastic dynamic programming problem and an airline fleet assignment problem . Although one can simply attempt a MARS approximation over all the variables , prior research on the fleet assignment application indicates that many variables have little effect on the objective . Thus , a data mining step to conduct variable selection is needed . This step separates potentially critical variables from clearly redundant ones . In this dissertation , variants of two data mining tools are explored separately and in combination for variable selection : regression trees and multiple procedures based on false discovery rate .
URI: http : / /hdl .handle .net /10106 /433
Date: 2007-08-23

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Convex Versions Of Multivariate Adaptive Regression Splines And Implementations For Complex Optimization Problems. Available electronically from http : / /hdl .handle .net /10106 /433 .

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