Determining optimal locations for charging stations of electric car-sharing systems under stochastic demand

  • Georg Brandstätter
  • Michael Kahr
  • Markus Leitner
    • Categories (Mixed) Integer Linear Programming, Transportation Tags , , , , ,

    In this article, we introduce and study a two-stage stochastic optimization problem suitable to solve strategic optimization problems of car-sharing systems that utilize electric cars. By combining the individual advantages of car-sharing and electric vehicles, such electric car-sharing systems may help to overcome future challenges related to pollution, congestion, or shortage of fossil fuels. A … Read more

    Linear Convergence of Proximal Incremental Aggregated Gradient Methods under Quadratic Growth Condition

  • Hui Zhang
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , , ,

    Under the strongly convex assumption, several recent works studied the global linear convergence rate of the proximal incremental aggregated gradient (PIAG) method for minimizing the sum of a large number of smooth component functions and a non-smooth convex function. In this paper, under the quadratic growth condition{a strictly weaker condition than the strongly convex assumption, … Read more

    Distributionally Robust Newsvendor Problems with Variation Distance

  • Hamed Rahimian
  • Güzin Bayraksan
  • Tito Homem-de-Mello
    • Categories Stochastic Programming

    We use distributionally robust stochastic programs (DRSPs) to model a general class of newsvendor problems where the underlying demand distribution is unknown, and so the goal is to find an order quantity that minimizes the worst-case expected cost among an ambiguity set of distributions. The ambiguity set consists of those distributions that are not far—in … Read more

    Optimal Storage and Transmission Investments in a Bilevel Electricity Market Model

  • Alexandra Märtz
  • Martin Weibelzahl
    • Categories Applications - OR and Management Sciences, Finance and Economics, Transportation Tags , , , , ,

    This paper analyzes the interplay of transmission and storage investments in a multistage game that we translate into a bilevel market model. In particular, on the first level we assume that a transmission system operator chooses an optimal line investment and a corresponding optimal network fee. On the second level we model competitive firms that … Read more

    On the Effects of Storage Facilities on Optimal Zonal Pricing in Electricity Markets

  • Alexandra Märtz
  • Martin Weibelzahl
    • Categories Applications - OR and Management Sciences, Finance and Economics, Transportation Tags , , ,

    This paper analyzes the effects of storage facilities on optimal zonal pricing in competitive electricity markets. In particular, we propose a zonal pricing model that comprises consumers, producers, and storage facilities on a network with constrained transmission capacities. In its two limit cases, our zonal pricing model includes the reference nodal pricing model as well … Read more

    A Novel Approach for Solving Convex Problems with Cardinality Constraints

  • Goran Banjac
  • Paul J. Goulart
    • Categories Approximation Algorithms Tags , , , ,

    In this paper we consider the problem of minimizing a convex differentiable function subject to sparsity constraints. Such constraints are non-convex and the resulting optimization problem is known to be hard to solve. We propose a novel generalization of this problem and demonstrate that it is equivalent to the original sparsity-constrained problem if a certain … Read more

    Co-optimization of Demand Response and Reserve Offers for a Major Consumer

  • Miguel F. Anjos
  • Anthony Downward
  • Michael C. Ferris
  • Mahbubeh Habibian
  • Golbon Zakeri
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Stochastic Programming Tags , ,

    In this paper we present a stochastic optimization problem for a strategic major consumer who has flexibility over its consumption and can offer reserve. Our model is a bi-level optimization model (reformulated as a mixed-integer program) that embeds the optimal power flow problem, in which electricity and reserve are co-optimized. We implement this model for … Read more

    A hybrid approach for Bi-Objective Optimization

  • Kim Allan Andersen
  • Thomas R. Stidsen
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches, Multi-Criteria Optimization

    A large number of the real world planning problems which are today solved using Operations Research methods are actually multi-objective planning problems, but most of them are solved using single-objective methods. The reason for converting, i.e. simplifying, multi- objective problems to single-objective problems is that no standard multi-objective solvers exist and specialized algorithms need to … Read more

    Plea for a semidefinite optimization solver in complex numbers

  • Jean Charles Gilbert
  • Cedric Josz
    • Categories Semi-definite Programming Tags , , ,

    Numerical optimization in complex numbers has drawn much less attention than in real numbers. A widespread opinion is that, since a complex number is a pair of real numbers, the best strategy to solve a complex optimization problem is to transform it into real numbers and to solve the latter by a real number solver. … Read more

    Radial Subgradient Descent

  • Benjamin Grimmer
    • Categories Convex Optimization Tags ,

    We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [1] by taking a different perspective, leading to an algorithm which is conceptually more natural, has notably improved convergence rates, and for which the analysis … Read more