Abstract: We survey recent results on the theory and algorithms of convex optimization, and its applications in large-scale optimization, inference/machine learning, signal processing,and large-scale and distributed optimization. We then focus on the class of incremental methods for problems involvingcost functions and constraints consisting of a large number of convex components. Ourmethods consist of iterations applied to single components, and haveproved very effective in practice. We introduce a unified algorithmicframework for a variety of such methods, some involving gradient andsubgradient iterations, which are known, and some involving combinationsof subgradient and proximal methods, which are new and offer greaterflexibility in exploiting special structure. We provide anoverview of the convergence and rate of convergence properties of thesemethods, including the  advantages offered by randomization in theselection of components, and we discuss their extensive applications.
Based on the books: "Convex Optimization Theory," Athena Scientific, 2009, and "Convex Optimization Algorithms," Athena Scientific, 2015.

by Dimitri P. Bertsekas, MIT教授，美国工程院院士

时间：3.31下午3点

地点：工商学院二楼报告厅