Robust Optimization

Maximum Likelihood Probability Measures over Sets and Applications to Data-Driven Optimization

  • Juan Borrero
  • Denis Saure
    • Categories Applications - OR and Management Sciences, Optimization in Data Science, Robust Optimization Tags , ,

    \(\) Motivated by data-driven approaches to sequential decision-making under uncertainty, we study maximum likelihood estimation of a distribution over a general measurable space when, unlike traditional setups, realizations of the underlying uncertainty are not directly observable but instead are known to lie within observable sets. While extant work studied the special cases when the observed … Read more

    Worst-Case Conditional Value at Risk for Asset Liability Management: A Novel Framework for General Loss Functions

  • Alireza Ghahtarani
  • Ahmed Saif
  • Alireza Ghasemi
    • Categories Applications - OR and Management Sciences, Finance and Economics, Robust Optimization Tags , , , ,

    Asset-liability management (ALM) is a challenging task faced by pension funds due to the uncertain nature of future asset returns and interest rates. To address this challenge, this paper presents a new mathematical model that uses aWorst-case Conditional Value-at-Risk (WCVaR) constraint to ensure that the funding ratio remains above a regulator-mandated threshold with a high … Read more

    Optimized Dimensionality Reduction for Moment-based Distributionally Robust Optimization

  • ShiyiJiang
  • Jianqiang Cheng
  • Kai Pan
  • Z.J. Max Shen
    • Categories Optimization in Data Science, Robust Optimization, Semi-definite Programming Tags , , , ,

    Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint distribution of random parameters runs in a distributional ambiguity set constructed by moment information and makes decisions against the worst-case distribution within the set. Although most moment-based DRO problems … Read more

    Differential Privacy via Distributionally Robust Optimization

  • Aras Selvi
  • Huikang Liu
  • Wolfram Wiesemann
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    In recent years, differential privacy has emerged as the de facto standard for sharing statistics of datasets while limiting the disclosure of private information about the involved individuals. This is achieved by randomly perturbing the statistics to be published, which in turn leads to a privacy-accuracy trade-off: larger perturbations provide stronger privacy guarantees, but they … Read more

    Data-driven distributionally robust optimization: Intersecting ambiguity sets, performance analysis and tractability

  • Neda Tanoumand
  • Merve Bodur
  • Joe Naoum-Sawaya
    • Categories Robust Optimization Tags , , ,

    We consider stochastic programs in which the probability distribution of uncertain parameters is unknown and partial information about it can only be captured from limited data. We use distributionally robust optimization (DRO) to model such problems. As opposed to the commonly used approach for DRO problems that suggests creating an ambiguity set by following a specific … Read more

    Multi-Stage Robust Mixed-Integer Programming

  • Krzysztof Postek
  • Ward Romeijnders
  • Wolfram Wiesemann
    • Categories (Mixed) Integer Linear Programming, Dynamic Programming, Robust Optimization Tags , ,

    Multi-stage robust optimization, in which decisions are taken sequentially as new information becomes available about the uncertain problem parameters, is a very versatile yet computationally challenging paradigm for decision-making under uncertainty. In this paper, we propose a new model and solution approach for multi-stage robust mixed-integer programs, which may contain both continuous and discrete decisions … Read more

    Robust Two-Dose Vaccination Schemes and the Directed b-Matching Problem

  • Jenny Segschneider
  • Arie M.C.A. Koster
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , , ,

    In light of the recent pandemic and the shortage of vaccinations during their roll-out, questions arose regarding the best strategy to achieve immunity throughout the population by adjusting the time gap between the two necessary vaccination doses. This strategy has already been studied from different angles by various researches. However, the deliveries of vaccination doses … Read more

    Robust two-stage combinatorial optimization problems under discrete demand uncertainties and consistent selection constraints

  • Sabrina Schmitz
  • Christina Büsing
    • Categories Robust Optimization Tags , , , ,

    In this paper, we study a robust two-stage concept of combinatorial optimization problems under discrete demand uncertainty. Combinatorial optimization problems are based on a finite set of elements for which we decide whether they are part of a solution. We divide the elements into two types, the so-called fixed and free elements. In a first … Read more

    Approximation Algorithms for Min-max-min Robust Optimization and K-Adaptability under Objective Uncertainty

  • Jannis Kurtz
    • Categories Approximation Algorithms, Robust Optimization Tags , , ,

    In this work we investigate the min-max-min robust optimization problem and the k-adaptability robust optimization problem for binary problems with uncertain costs. The idea of the first approach is to calculate a set of k feasible solutions which are worst-case optimal if in each possible scenario the best of the k solutions is implemented. It … Read more

    Two-stage and Lagrangian Dual Decision Rules for Multistage Adaptive Robust Optimization

  • Maryam Daryalal
  • Ayse Nur Arslan
  • Merve Bodur
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    In this work, we design primal and dual bounding methods for multistage adaptive robust optimization (MSARO) problems motivated by two decision rules rooted in the stochastic programming literature. From the primal perspective, this is achieved by applying decision rules that restrict the functional forms of only a certain subset of decision variables resulting in an … Read more