The robust stabilization problem for discrete-time descriptor systems

We investigate here the robust stabilization problem for the descriptor discrete time systems and build an optimal solution in the case when both the nominal system and the perturbations are given in terms of left coprime factorizations. Moreover our formulas are given straight from the original data, using solely the stabilizing solutions of two Riccati … Read more

Robust Unit Commitment with Dispatchable Wind: An LP Reformulation of the Second Stage

Abstract— The increasing penetration of uncertain generation such as wind and solar in power systems imposes new challenges to the Unit Commitment (UC) problem, one of the most critical tasks in power systems operations. The two most common approaches to address these challenges — stochastic and robust optimization — have drawbacks that prevent or restrict their … Read more

Multistage Adaptive Robust Optimization for the Unit Commitment Problem

The growing uncertainty associated with the increasing penetration of wind and solar power generation has presented new challenges to the operation of large-scale electric power systems. Motivated by these challenges, we present a multistage adaptive robust optimization model for the most critical daily operational problem of power systems, namely the unit commitment (UC) problem, in … Read more

Binary Decision Rules for Multistage Adaptive Mixed-Integer Optimization

Decision rules provide a flexible toolbox for solving the computationally demanding, multistage adaptive optimization problems. There is a plethora of real-valued decision rules that are highly scalable and achieve good quality solutions. On the other hand, existing binary decision rule structures tend to produce good quality solutions at the expense of limited scalability, and are … Read more

Robust risk adjustment in health insurance

Risk adjustment is used to calibrate payments to health plans based on the relative health status of insured populations and helps keep the health insurance market competitive. Current risk adjustment models use parameter estimates obtained via regression and are thus subject to estimation error. This paper discusses the impact of parameter uncertainty on risk scoring, … Read more

Robust Investment Management with Uncertainty in Fund Managers’ Asset Allocation

We consider a problem where an investment manager must allocate an available budget among a set of fund managers, whose asset allocations are not precisely known to the investment manager. In this paper, we propose a robust framework that takes into account the uncertainty stemming from the fund managers’ allocation, as well as the more … Read more

A Lagrangean Decomposition Approach for Robust Combinatorial Optimization

We address robust versions of combinatorial optimization problems, specializing on the discrete scenario case and the uncorrelated ellipsoidal uncertainty case. We present a branch and bound-algorithm for the min-max variant of these problems which uses lower bounds obtained from Lagrangean decomposition, allowing to separate the uncertainty aspect in the objective function from the combinatorial structure … Read more

Power-Capacity and Ramp-Capability Reserves for Wind Integration in Power-Based UC

This paper proposes a power-based network-constrained unit commitment (UC) model as an alternative to the traditional deterministic UCs to deal with wind generation uncertainty. The formulation draws a clear distinction between power-capacity and ramp-capability reserves to deal with wind production uncertainty. These power and ramp requirements can be obtained from wind forecast information. The model … Read more

Robust optimization criteria: state-of-the-art and new issues

Uncertain parameters appear in many optimization problems raised by real-world applications. To handle such problems, several approaches to model uncertainty are available, such as stochastic programming and robust optimization. This study is focused on robust optimization, in particular, the criteria to select and determine a robust solution. We provide an overview on robust optimization criteria … Read more

Robust newsvendor problem with autoregressive demand

This paper explores the classic single-item newsvendor problem under a novel setting which combines temporal dependence and tractable robust optimization. First, the demand is modeled as a time series which follows an autoregressive process AR(p), p>= 1. Second, a robust approach to maximize the worst-case revenue is proposed: a robust distribution-free autoregressive forecasting method, which … Read more