Research Projects

Semi-infinite programs (SIPs) arise naturally in a vast plethora of applications in machine learning, signal processing, control, robotics, and several other disciplines, wherein uncertainty in the underlying model of the optimization problem is unavoidable and robust solutions are essential. Convex SIPs constitute one of the most important subclasses of SIPs, and they arise naturally in robust linear, quadratic, semidefinite, and discrete optimization, mathematical programs with probabilistic constraints (chance and integrated chance constraints, CVaR constraints, etc.), and a host of other contexts. Despite their central importance and having been subjected to scrutiny for decades, convex SIPs are well-known to be difficult in terms of numerical tractability. This project leverages entirely new (and yet unpublished) results by the author and his students that provide a new approach to solving a broad class of convex SIPs near-optimally by means of targeted sampling of the constraints. From a practical standpoint, the accuracy of this technique depends only on the resources at one's disposal.