10:30 AM - 10:55 AM
Stability and continuity in robust linear and robust linear semi-infinite optimization
We present novel results on the stability of Robust Optimization (RO) problems with respect to perturbations in their uncertainty sets. We focus on Robust Linear and Robust Linear Semi-Infinite Optimization (LSIO) problems under cost function and constraint uncertainty, and prove Lipschitz continuity of the optimal value, and present results on the stability of the optimal solution set mapping and the ϵ-approximate optimal solution set mapping, all with respect to the Hausdorff distance between their uncertainty sets. Given the surge of interest in constructing data-driven uncertainty sets, our work provides an essential analysis of how the uncertainty set topology affects the optimal value and optimal solution set of a Robust Optimization problem.
10:55 AM - 11:20 AM
Practicable robust optimization for decomposable functions
Robust optimization (RO) is a powerful means to handle optimization problems where there is a set of parameters that are uncertain. The effectiveness of the method is especially noticeable when these parameters are only known to lie inside some uncertainty region. Unfortunately, there are important computational considerations that have prevented the methodology from being fully adopted in fields of practice where the cost function that needs to be "robustified" is nonlinear with respect to such parameters. In this paper, we propose a new robust optimization formulation that circumvent the computational burden in problems where the cost decomposes as the sum of convex costs for each decision variable. This is done by exploiting the fact that in this formulation the worst-case cost function can be expressed as a convex combination between a nominal and an upper-bound cost function. One can still control the conservatism of the robust solution by adjusting how many terms of the total cost function can simultaneously reach their respective most pessimistic value. In order to demonstrate the potential of our "practicable robust counterpart" formulation, we present how it can be employed on the robust optimization of packet routing on a telecommunication network with congestion.
11:20 AM - 11:45 AM
Robust optimization in R&D project selection
We discuss robust optimization models in the context of R&D project selection. The first part of the talk describes how tractable approximations to chance constraints can be used to develop an insightful RO framework. The second part of the talk focuses on designing and analyzing mathematical approaches that balance incremental and radical innovation.