2014/08/16 by Heinz H. Bauschke, Bauschke, Heinz H., Yves Lucet +3
Mathematics · #26B25 (Primary) 52A41 #65D17 #90C25 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Optimization and Control (math.OC) #math.CA #math.OC #msc:26B25 #msc:52A41 #msc:65D17 #msc:90C25
paper · pdf · doi:10.48550/arxiv.1408.3771
arxiv created 2014/08/16 · arxiv updated 2014/08/19
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.