A Method for Converting a Class of Univariate Functions into D.C. Functions

Authors:
Bruce W. Lamar
Affiliations:
Economic and Decision Analysis Center, The MITRE Corporation, Bedford, Massachusetts, USA (fax: 781 2716939/ e-mail: bwlamar@mitre.org)
Venue:
Journal of Global Optimization
Year:
1999

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Abstract

D.c. functions are functions that can be expressed as the sum of a concave function and a convex function (or as the difference of two convex functions). In this paper, we extend the class of univariate functions that can be represented as d.c. functions. This expanded class is very broad including a large number of nonlinear and/or ’nonsmooth‘ univariate functions. In addition, the procedure specifies explicitly the functional and numerical forms of the concave and convex functions that comprise the d.c. representation of the univariate functions. The procedure is illustrated using two numerical examples. Extensions of the conversion procedure for discontinuous univariate functions is also discussed.