A Comment on “Computational Complexity of Stochastic Programming Problems”

Although stochastic programming problems were always believed to be computationally challenging, this perception has only recently received a theoretical justification by the seminal work of Dyer and Stougie (Mathematical Programming A, 106(3):423–432, 2006). Amongst others, that paper argues that linear two-stage stochastic programs with fixed recourse are #P-hard even if the random problem data is … Read more

Robust Growth-Optimal Portfolios

The growth-optimal portfolio is designed to have maximum expected log-return over the next rebalancing period. Thus, it can be computed with relative ease by solving a static optimization problem. The growth-optimal portfolio has sparked fascination among finance professionals and researchers because it can be shown to outperform any other portfolio with probability 1 in the … Read more

K-Adaptability in Two-Stage Robust Binary Programming

Over the last two decades, robust optimization has emerged as a computationally attractive approach to formulate and solve single-stage decision problems affected by uncertainty. More recently, robust optimization has been successfully applied to multi-stage problems with continuous recourse. This paper takes a step towards extending the robust optimization methodology to problems with integer recourse, which … Read more

Interdiction Games on Markovian PERT Networks

In a stochastic interdiction game a proliferator aims to minimize the expected duration of a nuclear weapons development project, while an interdictor endeavors to maximize the project duration by delaying some of the project tasks. We formulate static and dynamic versions of the interdictor’s decision problem where the interdiction plan is either pre-committed or adapts … Read more

Distributionally Robust Convex Optimization

Distributionally robust optimization is a paradigm for decision-making under uncertainty where the uncertain problem data is governed by a probability distribution that is itself subject to uncertainty. The distribution is then assumed to belong to an ambiguity set comprising all distributions that are compatible with the decision maker’s prior information. In this paper, we propose … Read more

Pessimistic Bi-Level Optimisation

Bi-level problems are optimisation problems in which some of the decision variables must optimise a subordinate (lower-level) problem. In general, the lower-level problem can possess multiple optimal solutions. One therefore distinguishes between optimistic formulations, which assume that the most favourable lower-level solution is implemented, and pessimistic formulations, in which the most adverse lower-level solution is … Read more

The Decision Rule Approach to Optimization under Uncertainty: Methodology and Applications

Dynamic decision-making under uncertainty has a long and distinguished history in operations research. Due to the curse of dimensionality, solution schemes that naively partition or discretize the support of the random problem parameters are limited to small and medium-sized problems, or they require restrictive modeling assumptions (e.g., absence of recourse actions). In the last few … Read more

Generalized Decision Rule Approximations for Stochastic Programming via Liftings

Stochastic programming provides a versatile framework for decision-making under uncertainty, but the resulting optimization problems can be computationally demanding. It has recently been shown that, primal and dual linear decision rule approximations can yield tractable upper and lower bounds on the optimal value of a stochastic program. Unfortunately, linear decision rules often provide crude approximations … Read more

Robust Markov Decision Processes

Markov decision processes (MDPs) are powerful tools for decision making in uncertain dynamic environments. However, the solutions of MDPs are of limited practical use due to their sensitivity to distributional model parameters, which are typically unknown and have to be estimated by the decision maker. To counter the detrimental effects of estimation errors, we consider … Read more

Robust Software Partitioning with Multiple Instantiation

The purpose of software partitioning is to assign code segments of a given computer program to a range of execution locations such as general purpose processors or specialist hardware components. These execution locations differ in speed, communication characteristics, and in size. In particular, hardware components offering high speed tend to accommodate only few code segments. … Read more