trees

A Parametric Approach for Solving Convex Quadratic Optimization with Indicators Over Trees

  • Aaresh Bhathena
  • Salar Fattahi
  • Andrés Gómez
  • Simge Küçükyavuz
    • Categories (Mixed) Integer Nonlinear Programming, Dynamic Programming, Quadratic Programming Tags , , , , ,

    This paper investigates convex quadratic optimization problems involving $n$ indicator variables, each associated with a continuous variable, particularly focusing on scenarios where the matrix $Q$ defining the quadratic term is positive definite and its sparsity pattern corresponds to the adjacency matrix of a tree graph. We introduce a graph-based dynamic programming algorithm that solves this … Read more

    Tree Bounds for Sums of Bernoulli Random Variables: A Linear Optimization Approach

  • Karthik Natarajan
  • Divya Padmanabhan
    • Categories Combinatorial Optimization, Linear, Cone and Semidefinite Programming, Robust Optimization Tags , ,

    We study the problem of computing the tightest upper and lower bounds on the probability that the sum of n dependent Bernoulli random variables exceeds an integer k. Under knowledge of all pairs of bivariate distributions denoted by a complete graph, the bounds are NP-hard to compute. When the bivariate distributions are specified on a … Read more

    Bookings in the European Gas Market: Characterisation of Feasibility and Computational Complexity Results

  • Martine Labbé
  • Martin Schmidt
  • Fränk Plein
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Network Optimization Tags , , , , ,

    As a consequence of the liberalisation of the European gas market in the last decades, gas trading and transport have been decoupled. At the core of this decoupling are so-called bookings and nominations. Bookings are special capacity right contracts that guarantee that a specified amount of gas can be supplied or withdrawn at certain entry … Read more

    Location Routing Problems on Simple Graphs

  • Julian Araoz
  • Elena Fernandez
    • Categories Combinatorial Optimization Tags , ,

    This paper addresses combined location/routing problems defined on trees. Several problems are studied, which consider service demand both at the vertices and the edges of the input tree. Greedy type optimal heuristics are presented for the cases when all vertices have to be visited and facilities have no set-up costs. Facilities set-up costs can also … Read more

    Speeding up dynamic shortest path algorithms

  • Luciana S. Buriol
  • Mauricio G.C. Resende
  • Mikkel Thorup
    • Categories Network Optimization Tags , , , ,

    Dynamic shortest path algorithms update the shortest paths to take into account a change in an edge weight. This paper describes a new technique that allows the reduction of heap sizes used by several dynamic shortest path algorithms. For unit weight change, the updates can be done without heaps. These reductions almost always reduce the … Read more