A Tractable Approximation of Stochastic Programming via Robust Optimization

Stochastic programming, despite its immense modeling capabilities, is well known to be computationally excruciating. In this paper, we introduce a unified framework of approximating multiperiod stochastic programming from the perspective of robust optimization. Specifically, we propose a framework that integrates multistage modeling with safeguarding constraints. The framework is computationally tractable in the form of second … Read more

A Robust Optimization Framework for Analyzing Distribution Systems with Transshipment

This paper studies a distribution system consisting of multiple retail locations with transshipment operations among the retailers. Due to the difficulty in computing the optimal solution imposed by the transshipment operations and in estimating shortage cost from a practical perspective, we propose a robust optimization framework for analyzing the impact of transshipment operations on such … Read more

Single-Product Pricing via Robust Optimization

We present a robust optimization approach to the problem of pricing a capacitated product over a finite time horizon in the presence of demand uncertainty. This technique does not require the knowledge of the underlying probability distributions, which in practice are difficult to estimate accurately, and instead models random variables as uncertain parameters belonging to … Read more

Efficient Schemes for Robust IMRT Treatment Planning

We use robust optimization techniques to formulate an IMRT treatment planning problem in which the dose matrices are uncertain, due to both dose calculation errors and inter-fraction positional uncertainty of tumor and organs. When the uncertainty is taken into account, the original linear programming formulation becomes a second-order cone program. We describe a novel and … Read more

Prox-Regularity and Stability of the Proximal Mapping

Fundamental insights into the properties of a function come from the study of its Moreau envelopes and Proximal point mappings. In this paper we examine the stability of these two objects under several types of perturbations. In the simplest case, we consider tilt-perturbations, i.e. perturbations which correspond to adding a linear term to the objective … Read more

On Ants, Bacteria and Dynamic Environments

Wasps, bees, ants and termites all make effective use of their environment and resources by displaying collective “swarm” intelligence. Termite colonies – for instance – build nests with a complexity far beyond the comprehension of the individual termite, while ant colonies dynamically allocate labor to various vital tasks such as foraging or defense without any … Read more

Efficient Robust Optimization for Robust Control with Constraints

This paper proposes an efficient computational technique for the optimal control of linear discrete-time systems subject to bounded disturbances with mixed polytopic constraints on the states and inputs. The problem of computing an optimal state feedback control policy, given the current state, is non-convex. A recent breakthrough has been the application of robust optimization techniques … Read more

Constructing Risk Measures from Uncertainty Sets

We propose a unified theory that links uncertainty sets in robust optimization to risk measures in portfolio optimization. We illustrate the correspondence between uncertainty sets and some popular risk measures in finance, and show how robust optimization can be used to generalize the concepts of these measures. We also show that by using properly defined … Read more

A General Robust-Optimization Formulation for Nonlinear Programming

Most research in robust optimization has so far been focused on inequality-only, convex conic programming with simple linear models for uncertain parameters. Many practical optimization problems, however, are nonlinear and non-convex. Even in linear programming, coefficients may still be nonlinear functions of uncertain parameters. In this paper, we propose robust formulations that extend the robust-optimization … Read more

A Robust Optimization Perspective of Stochastic Programming

In this paper, we introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for bounded random variables known as the forward and backward deviations. These deviation measures capture distributional asymmetry and lead to better approximations of chance constraints. We also propose a tractable robust optimization approach for obtaining robust solutions … Read more