Mathematics, University of British Columbia
B.C. V1V 1V7,
2 Computer Science, University of British Columbia Okanagan, Kelowna, B.C. V1V 1V7, Canada.
3 Department of Mathematical Sciences, University of Massachusetts Lowell, Lowell, M.A. 01854, USA.
Revised: 27 March 2015
Functions that are piecewise defined are a common sight in mathematics while convexity is a property especially desired in optimization. Suppose now a piecewise-defined function is convex on each of its defining components – when can we conclude that the entire function is convex? In this paper we provide several convenient, verifiable conditions guaranteeing convexity (or the lack thereof). Several examples are presented to illustrate our results.
Mathematics Subject Classification: 26B25 / 52A41 / 65D17 / 90C25
Key words: Computer-aided convex analysis / convex function / convex interpolation / convex set / piecewise-defined function
HHB was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada under Discovery Grant #216877-2013 and by the Canada Research Chair Program.
© EDP Sciences, SMAI 2016