Online Combinatorial Optimization Problems with Non-linear Objectives

Abstract

We survey some recent progress on the design and the analysis of online algorithms for optimization problems with non-linear, usually convex, objectives. We focus on an extension of the online primal dual technique, and highlight its application in a number of applications, including an online matching problem with concave returns, an online scheduling problem with speed-scalable machines subjective to convex power functions, and a family of online covering and packing problems with convex objectives.