It is well-known that the second-order cone can be outer-approximated to an arbitrary accuracy by a polyhedral cone of compact size defined by irrational data. In this paper, we propose two rational polyhedral outer-approximations of compact size retaining the same guaranteed accuracy. The first outer-approximation has the same size as the optimal but irrational outer-approximation … Read more
We consider the problem of estimating the true values of a Wiener process given noisy observations corrupted by outliers. The problem considered is closely related to the Trimmed Least Squares estimation problem, a robust estimation procedure well-studied from a statistical standpoint but poorly understood from an optimization perspective. In this paper we show how to … Read more
The application of mathematical optimization methods provides the capacity to increase the energy efficiency and to lower the investment costs of technical systems, considerably. We present a system approach for the optimization of the design and operation of pumping systems and exemplify it by applying it to the water supply of high-rise buildings. The underlying … Read more
The paper overviews stochastic optimization models of insurance mathematics and methods for their solution from the point of view of stochastic programming and stochastic optimal control methodology, with vector optimality criteria. The evolution of an insurance company’s capital is considered in discrete time. The main random variables, which influence this evolution, are levels of payments, … Read more
The Unit Commitment (UC) problem in electrical power production requires to optimally operate a set of power generation units over a short time horizon (one day to a week). Operational constraints of each unit depend on its type (e.g., thermal, hydro, nuclear, …), and can be rather complex. For thermal units, typical ones concern minimum … Read more
We give an explicit geometric way to build mixed-integer programming (MIP) formulations for unions of polyhedra. The construction is simply described in terms of spanning hyperplanes in an r-dimensional linear space. The resulting MIP formulation is ideal, and uses exactly r integer variables and 2 x (# of spanning hyperplanes) general inequality constraints. We use … Read more
Benders’ decomposition is a popular mathematical and constraint programming algorithm that is widely applied to exploit problem structure arising from real-world applications. While useful for exploiting structure in mathematical and constraint programs, the use of Benders’ decomposition typically requires significant implementation effort to achieve an effective solution algorithm. Traditionally, Benders’ decomposition has been viewed as … Read more
We compare various flexible tariffs that have been proposed to cost-effectively govern a prosumer’s electricity management – in particular time-of-use (TOU), critical-peak-pricing (CPP), and a real-time-pricing tariff (RTP). As the outside option, we consider a fixed-price tariff (FP) that restricts the specific characteristics of TOU, CPP, and RTP, so that the flexible tariffs are at … Read more
We introduce the Stochastic Maintenance Fleet Transportation Problem for Offshore wind farms (SMFTPO), in which a maintenance provider determines an optimal, medium-term planning for maintaining multiple wind farms while controlling for uncertainty in the maintenance tasks and weather conditions. Since the maintenance provider is typically not the owner of a wind farm, it needs to … Read more
Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized PDEs. So far, the Branch-and-Bound framework has been the most common solution strategy for such problems. In order to provide an alternative solution approach, especially … Read more