Growth-optimal portfolios are guaranteed to accumulate higher wealth than any other investment strategy in the long run. However, they tend to be risky in the short term. For serially uncorrelated markets, similar portfolios with more robust guarantees have been recently proposed. This paper extends these robust portfolios by accommodating non-zero autocorrelations that may reflect investors’ … Read more
We consider the finite horizon inventory routing problem with uncertain demand, where a supplier must deliver a particular commodity to its customers periodically, such that even under uncertain demand the customers do not stock out, e.g. supplying residential heating oil to customers. Current techniques that solve this problem with stochastic demand, robust or adaptive optimization … Read more
In recent papers, we have shown that a Lebesgue-Stieltjes optimal control theory forms the foundations for unscented optimal control. In this paper, we further our results by incorporating uncertain mixed state-control constraints in the problem formulation. We show that the integrated Hamiltonian minimization condition resembles a semi-infinite type mathematical programming problem. The resulting computational difficulties … Read more
The problem of identifying a specific design or architecture that allows to satisfy all the system requirements becomes more difficult when uncertainties are taken into account. When a requirement is subject to uncertainty there are a number approaches available to the system engineer, each one with its own benefits and disadvantages. Classical robust optimization is … Read more
Distributionally robust optimization (DRO) is widely used, because it offers a way to overcome the conservativeness of robust optimization without requiring the specificity of stochastic optimization. On the computational side, many practical DRO instances can be equivalently (or approximately) formulated as semidefinite programming (SDP) problems via conic duality of the moment problem. However, despite being … Read more
This paper proposes a multi-stage stochastic programming formulation for the reservoir management problem. Our problem specifically consists in minimizing the risk of floods over a fixed time horizon for a multi-dimensional hydro-electrical complex. We consider well-studied linear time series model and enhance the approach to consider heteroscedasticity. Using these stochastic processes under very general distributional … Read more
The deep penetration of wind and solar power is a critical component of the future power grid. However, the intermittency and stochasticity of these renewable resources bring significant challenges to the reliable and economic operation of power systems. Motivated by these challenges, we present a multistage adaptive robust optimization model for the unit commitment (UC) … Read more
In this paper we study systems that allocate different types of scarce resources to heterogeneous allocatees based on predetermined priority rules, e.g., the U.S. deceased-donor kidney allocation system or the public housing program. We tackle the problem of estimating the wait time of an allocatee who possesses incomplete system information with regard, for example, to … Read more
Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is an underlying probability distribution that is known exactly, one hedges against a chosen set of distributions. In this paper, we consider sets of distributions that are within a chosen Wasserstein distance from a nominal distribution. … Read more
In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method extends in a natural way a linearization scheme that was recently proposed to construct tractable reformulations for robust static problems involving profit functions that decompose as a sum of piecewise linear concave expressions. Given that … Read more