In \cite{siebert2019linear} the authors present a set of integer programs (IPs) for the Steiner tree problem, which can be used for both, the directed and the undirected setting of the problem. Each IP finds an optimal Steiner tree with a specific structure. A solution with the lowest cost, corresponds to an optimal solution to the … Read more
In this paper, we consider the problem of equal risk pricing and hedging in which the fair price of an option is the price that exposes both sides of the contract to the same level of risk. Focusing for the first time on the context where risk is measured according to convex risk measures, we … Read more
The recent growth of direct-to-consumer deliveries has stressed the importance of last-mile logistics, becoming one of the critical factors in city planning. One of the key factors lies in the last-mile deliveries, reaching in some cases nearly 50% of the overall parcel delivery cost. Different variants of the the well-known Traveling Salesman Problem (TSP) arise … Read more
In this paper we go one step further in the automatic generation of FPTASes for multi-stage stochastic dynamic programs with scalar state and action spaces, in where the cost-to-go functions have a monotone structure in the state variable. While there exist a few frameworks for automatic generation of FPTASes, so far none of them is … 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
In this work, nonconvex nonsmooth problems of dynamic optimization, optimal control in discrete time (including feedback control), and machine learning are considered from a common point of view. An analogy is observed between tasks of controlling discrete dynamic systems and training multilayer neural networks with nonsmooth target function and connections. Methods for calculating generalized gradients … Read more
In some applications the considered multistage stochastic programs have a periodical behavior. We show that in such cases it is possible to drastically reduce the number of stages by introducing a periodical analog of the so-called Bellman equations for discounted infinite horizon problems, used in Markov Decision Processes and Stochastic Optimal Control. Furthermore, we describe … Read more
We propose a new algorithm for solving multistage stochastic mixed integer linear programming (MILP) problems with complete continuous recourse. In a similar way to cutting plane methods, we construct nonlinear Lipschitz cuts to build lower approximations for the non-convex cost to go functions. An example of such a class of cuts are those derived using … Read more
The valuation of a real option is preferably done with the inclusion of uncertainties in the model, since the value depends on future costs and revenues, which are not perfectly known today. The usual value of the option is defined as the maximal expected (discounted) profit one may achieve under optimal management of the operation. … Read more