On the pervasiveness of difference-convexity in optimization and statistics (Q1739035)

Functions, which can be expressed as a difference of two convex functions are called dc-functions. Such functions are in general non-convex, nevertheless, their special structure makes possible successful applying the functions in many areas of operations research. The authors consider functions, which arise from the following three application areas: 1. composite risk functionals; 2. statistical estimation and learning; 3. quadratic recourse in stochastic programming. These functions were not prevously known to belong to dc-functions. The authors establish conditions under which the considered functions belong to the class of dc-functions. Possibilities of further usage of the obtained results are briefly discussed.