Explicit reformulations for robust optimization problems with general uncertainty sets

We consider a rather general class of mathematical programming problems with data uncertainty, where the uncertainty set is represented by a system of convex inequalities. We prove that the robust counterparts of this class of problems can be equivalently reformulated as finite and explicit optimization problems. Moreover, we develop simplified reformulations for problems with uncertainty … Read more

Tractable algorithms for chance-constrained combinatorial problems

This paper aims at proposing tractable algorithms to find effectively good solutions to large size chance-constrained combinatorial problems. A new robust model is introduced to deal with uncertainty in mixed-integer linear problems. It is shown to be strongly related to chance-constrained programming when considering pure 0-1 problems. Furthermore, its tractability is highlighted. Then, an optimization … Read more

The Value of Information in Inventory Management

Inventory management traditionally assumes the precise knowledge of the underlying demand distribution and a risk-neutral manager. New product introduction does not fit this framework because (i) not enough information is available to compute probabilities and (ii) managers are generally risk-averse. In this work, we analyze the value of information for two-stage inventory management in a … Read more

Robust Inventory Management Using Tractable Replenishment Policies

We propose tractable replenishment policies for a multi-period, single product inventory control problem under ambiguous demands, that is, only limited information of the demand distributions such as mean, support and deviation measures are available. We obtain the parameters of the tractable replenishment policies by solving a deterministic optimization problem in the form of second order … Read more

An estimation-free, robust conditional value-at-risk portfolio allocation model

We propose a novel optimization model for risk-averse investors to obtain robust solutions for portfolio allocation problems. Unlike related models in the literature, no historical data or statistical estimation techniques are used to compute the parameters of the model. Instead, the parameters are directly obtained from current prices of options on the assets being considered. … Read more

Separation of convex polyhedral sets with uncertain data

This paper is a contribution to the interval analysis and separability of convex sets. Separation is a familiar principle and is often used not only in optimization theory, but in many economic applications as well. In real problems input data are usually not known exactly. For the purpose of this paper we assume that data … Read more

Experiments in Robust Portfolio Optimization

We present experimental results on portfolio optimization problems with return errors under the robust optimization framework. We use several a histogram-like model for return deviations, and a model that allows correlation among errors, together with a cutting-plane algorithm which proves effective for large, real-life data sets. Citation Columbia Center for Financial Engineering Report 2007-01 Columbia … Read more

Constrained linear system with disturbance: stability under disturbance feedback

This paper proposes a control parametrization under Model Predictive Controller (MPC) framework for constrained linear discrete time systems with bounded additive disturbances. The proposed approach has the same feasible domain as that obtained from parametrization over the family of time-varying state feedback policies. In addition, the closed-loop system is stable in the sense that the … Read more

From CVaR to Uncertainty Set: Implications in Joint Chance Constrained Optimization

In this paper we review the different tractable approximations of individual chance constraint problems using robust optimization on a varieties of uncertainty set, and show their interesting connections with bounds on the condition-value-at-risk CVaR measure popularized by Rockafellar and Uryasev. We also propose a new formulation for approximating joint chance constrained problems that improves upon … Read more

A New Cone Programming Approach for Robust Portfolio Selection

The robust portfolio selection problems have recently been studied by several researchers (e.g., see \cite{GoIy03,ErGoIy04,HaTu04,TuKo04}). In their work, the “separable” uncertainty sets of the problem parameters (e.g., mean and covariance of the random returns) were considered. These uncertainty sets share two common drawbacks: i) the actual confidence level of the uncertainty set is unknown, and … Read more