摘要

Convex optimization was radically transformed following Fenchel's work (1951), and was articulated by Rockafellar in his classic text (1970). Yet, some of the fundamental underpinnings of the field have remained poorly understood, because of the difficulty of the analysis and the lack of unification. On the algorithmic side, convex optimization has found increasing use in important and large scale problems, arising in optimal resource allocation, engineering design, machine learning, optimal control, and combinatorial optimization.

This talk will review a new textbook ("Convex Optimization Theory" by D. Bertsekas, 2009) and a 2003 predecessor, which aim to restructure the fundamental duality theory underlying the subject using a handful of unifying principles that can be easily visualized and readily understood.  This leads to a unified development of duality for several important types of problems, such as constrained optimization and minimax, as special cases of duality between two simple geometrical problems. A followup talk will discuss convex optimization algorithms.

演讲人简历

Dimitri P. Bertsekas received his undergraduate degree in engineering from the National Technical University of Athens, Greece, and his Ph.D. from the Massachusetts Institute of Technology.