Affine Decision Rule Approximation to Immunize against Demand Response Uncertainty in Smart Grids’ Capacity Planning

  • Sajad Aliakbari-Sani
  • Olivier Bahn
  • Erick Delage
    • Categories Energy, Linear Programming, Robust Optimization Tags , , ,

    Generation expansion planning (GEP) is a classical problem that determines an optimal investment plan for existing and future electricity generation technologies. GEP is a computationally challenging problem, as it typically corresponds to a very large-scale problem that contains several sources of uncertainties. With the advent of demand response (DR) as a reserved capacity in modern … Read more

    A Polyhedral Study for the Cubic Formulation of the Unconstrained Traveling Tournament Problem

  • Marije Siemann
  • Matthias Walter
    • Categories Applications - OR and Management Sciences, Polyhedra Tags ,

    We consider the unconstrained traveling tournament problem, a sports timetabling problem that minimizes traveling of teams. Since its introduction about 20 years ago, most research was devoted to modeling and reformulation approaches. In this paper we carry out a polyhedral study for the cubic integer programming formulation by establishing the dimension of the integer hull … Read more

    Simple Iterative Methods for Linear Optimization over Convex Sets

  • Daniel Dadush
  • Christopher Hojny
  • Sophie Huiberts
  • Stefan Weltge
    • Categories Linear Programming Tags , ,

    We give simple iterative methods for computing approximately optimal primal and dual solutions for the problem of maximizing a linear functional over a convex set $K$ given by a separation oracle. In contrast to prior work, our algorithms directly output primal and dual solutions and avoid a common requirement of binary search on the objective … Read more

    Contextual Chance-Constrained Programming

  • Hamed Rahimian
  • Bernardo K. Pagnoncelli
    • Categories Stochastic Programming Tags , , , ,

    Uncertainty in classical stochastic programming models is often described solely by independent random parameters, ignoring their dependence on multidimensional features. We describe a novel contextual chance-constrained programming formulation that incorporates features, and argue that solutions that do not take them into account may not be implementable. Our formulation cannot be solved exactly in most cases, … Read more

    Compact mixed-integer programming relaxations in quadratic optimization

  • Ben Beach
  • Robert Hildebrand
  • Joey Huchette
    • Categories (Mixed) Integer Nonlinear Programming, 0-1 Programming, Global Optimization

    We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this (simple) approximation using mixed-integer programming (MIP). Notably, the number of constraints, binary variables, and auxiliary continuous variables used in this formulation grows logarithmically in … Read more

    Cost-Sharing Mechanism Design for Ride-Sharing

  • Maged M. Dessouky
  • Nelson A. Uhan
  • Shichun Hu
  • Phebe Vayanos
    • Categories Game Theory, Transportation

    In this paper, we focus on the cost-sharing problem for ride-sharing that determines how to allocate the total ride cost between the driver and the passengers. We identify the properties that a desirable cost-sharing mechanism should have and develop a general framework which can be used to create specific cost-sharing mechanisms. We propose specific mechanisms … Read more

    Amenable cones are particularly nice

  • Bruno F. Lourenço
  • Vera Roshchina
  • James Saunderson
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming

    Amenability is a geometric property of convex cones that is stronger than facial exposedness and assists in the study of error bounds for conic feasibility problems. In this paper we establish numerous properties of amenable cones, and investigate the relationships between amenability and other properties of convex cones, such as niceness and projectional exposure. We … Read more

    Decentralized Failure-Tolerant Optimization of Electric Vehicle Charging

  • Ignacio Aravena
  • Steve Chaping
  • Colin Ponce
    • Categories Convex Optimization, Energy, Scheduling Tags , , ,

    We present a decentralized failure-tolerant algorithm for optimizing electric vehicle (EV) charging, using charging stations as computing agents. The algorithm is based on the alternating direction method of multipliers (ADMM) and it has the following features: (i) It handles capacity, peak demand, and ancillary services coupling constraints. (ii) It does not require a central agent … Read more

    A Primal-Dual Algorithm for Risk Minimization

  • Drew P. Kouri
  • Thomas Surowiec
    • Categories Infinite Dimensional Optimization, Nonsmooth Optimization, Stochastic Programming Tags , , ,

    In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is … Read more

    On Generating Lagrangian Cuts for Two-stage Stochastic Integer Programs

  • Rui Chen
  • James R. Luedtke
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , ,

    We investigate new methods for generating Lagrangian cuts to solve two-stage stochastic integer programs. Lagrangian cuts can be added to a Benders reformulation, and are derived from solving single scenario integer programming subproblems identical to those used in the nonanticipative Lagrangian dual of a stochastic integer program. While Lagrangian cuts have the potential to significantly … Read more