Mean-variance (MV) analysis is often sensitive to model mis-specification or uncertainty, meaning that the MV efficient portfolios constructed with an estimate of the model parameters (i.e., the expected return vector and covariance of asset returns) can give very poor performance for another set of parameters that is similar and statistically hard to distinguish from the … Read more
This paper concerns a fractional function of the form $x^Ta/\sqrt{x^TBx}$, where $B$ is positive definite. We consider the game of choosing $x$ from a convex set, to maximize the function, and choosing $(a,B)$ from a convex set, to minimize it. We prove the existence of a saddle point and describe an efficient method, based on … Read more
In engineering design, an optimized solution often turns out to be suboptimal, when implementation errors are encountered. While the theory of robust convex optimization has taken significant strides over the past decade, all approaches fail if the underlying cost function is not explicitly given; it is even worse if the cost function is nonconvex. In … Read more
This paper presents a three-stage optimization algorithm for solving two-stage robust decision making problems under uncertainty with min-max regret objective. The structure of the first stage problem is a general mixed integer (binary) linear programming model with a specific model of uncertainty that can occur in any of the parameters, and the second stage problem … Read more
Robust optimization programs are hard to solve even when the constraints are convex. In previous contributions, it has been shown that approximately robust solutions (i.e. solutions feasible for all constraints but a small fraction of them) to convex programs can be obtained at low computational cost through constraints randomization. In this paper, we establish new … Read more
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
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
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
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
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