University of California at Berkeley Robust optimization deals with
optimization problems in which the data (say, the coefficients in a linear
program) are only known within a set, and a decision variable guaranteed
to satisfy all the constraints despite data uncertainty is sought. We
describe the main results in robust optimization, in particular how
second-order cone or semidefinite programming relaxations can be used to
obtain robust solutions to uncertain programs. We explore connections
between the robust (or worst-case) approach and stochastic descriptions of
uncertainty, in which the distribution of the uncertainty is partially
known. We then give an overview of applications, ranging from control
systems (robust control of uncertain dynamical systems) to machine
learning (robust classification, support vector machines, and kernel
optimization). |