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

Extending Scope of Robust Optimization: Comprehensive Robust Counterparts of Uncertain Problems

In this paper, we propose a new methodology for handling optimization problems with uncertain data. With the usual Robust Optimization paradigm, one looks for the decisions ensuring a required performance for all realizations of the data from a given bounded uncertainty set, whereas with the proposed approach, we require also a controlled deterioration in performance … Read more

Robust DWDM Routing and Provisioning under Polyhedral Demand Uncertainty

We present mixed integer linear programming models that are robust in the face of uncertain traffic demands known to lie in a certain polyhedron for the problem of dense wavelength division multiplexing network routing and provisioning at minimal cost. We investigate the solution of the problem in a set of numerical experiments for two models … Read more

Provisioning Virtual Private Networks under traffic uncertainty

We investigate a network design problem under traffic uncertainty which arises when provisioning Virtual Private Networks (VPNs): given a set of terminals that must communicate with one another, and a set of possible traffic matrices, sufficient capacity has to be reserved on the links of the large underlying public network so as to support all … Read more