inverse optimization

Estimating the Unobservable Components of Electricity Demand Response with Inverse Optimization

  • Adrian Esteban Perez
    • Categories Energy, Statistics, Stochastic Programming Tags , , , , ,

    Understanding and predicting the electricity demand responses to prices are critical activities for system operators, retailers, and regulators. While conventional machine learning and time series analyses have been adequate for the routine demand patterns that have adapted only slowly over many years, the emergence of active consumers with flexible assets such as solar-plus-storage systems, and … Read more

    Inverse of the Gomory Corner Relaxation of Integer Programs

  • Fatemeh Nosrat
  • George Lyu
  • Andrew J. Schaefer
    • Categories (Mixed) Integer Linear Programming, Integer Programming, Other Topics Tags , , ,

    We analyze the inverse of the Gomory corner relaxation (GCR) of a pure integer program (IP). We prove the inverse GCR is equivalent to the inverse of a shortest path problem, yielding a polyhedral representation of the GCR inverse-feasible region. We present a linear programming (LP) formulation for solving the inverse GCR under the \(L_{1}\) … Read more

    Counterfactual Explanations for Linear Optimization

  • Jannis Kurtz
  • Ş. İlker Birbil
  • Dick den Hertog
    • Categories Applications - OR and Management Sciences, Linear Programming Tags , , ,

    The concept of counterfactual explanations (CE) has emerged as one of the important concepts to understand the inner workings of complex AI systems. In this paper, we translate the idea of CEs to linear optimization and propose, motivate, and analyze three different types of CEs: strong, weak, and relative. While deriving strong and weak CEs … Read more

    Learning in Inverse Optimization: Incenter Cost, Augmented Suboptimality Loss, and Algorithms

  • Pedro Zattoni Scroccaro
  • Bilge Atasoy
  • Peyman Mohajerin Esfahani
    • Categories Convex and Nonsmooth Optimization Tags ,

    In Inverse Optimization (IO), an expert agent solves an optimization problem parametric in an exogenous signal. From a learning perspective, the goal is to learn the expert’s cost function given a dataset of signals and corresponding optimal actions. Motivated by the geometry of the IO set of consistent cost vectors, we introduce the “incenter” concept, … Read more

    Hidden convexity in a class of optimization problems with bilinear terms

  • Bram L. Gorissen
  • Meike Reusken
  • Dick den Hertog
    • Categories Nonlinear Optimization, Robust Optimization Tags , , ,

    In this paper we identify a new class of nonconvex optimization problems that can be equivalently reformulated to convex ones. These nonconvex problems can be characterized by convex functions with bilinear arguments. We describe several examples of important applications that have this structure. A reformulation technique is presented which converts the problems in this class … Read more