SDP-based bounds for the Quadratic Cycle Cover Problem via cutting plane augmented Lagrangian methods and reinforcement learning

  • Frank de Meijer
  • Renata Sotirov
    • Categories Combinatorial Optimization, Semi-definite Programming Tags , , , , ,

    We study the Quadratic Cycle Cover Problem (QCCP), which aims to find a node-disjoint cycle cover in a directed graph with minimum interaction cost between successive arcs. We derive several semidefinite programming (SDP) relaxations and use facial reduction to make these strictly feasible. We investigate a nontrivial relationship between the transformation matrix used in the … Read more

    The Non-Stop Disjoint Trajectories Problem

  • Benno Hoch
  • Frauke Liers
  • Sarah Neumann
  • Francisco Javier Zaragoza Martínez
    • Categories Combinatorial Optimization, Network Optimization Tags , , , , ,

    Consider an undirected network with traversal times on its edges and a set of commodities with connection requests from sources to destinations and release dates. The non-stop disjoint trajectories problem is to find trajectories that fulfill all requests, such that the commodities never meet. In this extension to the \NP-complete disjoint paths problem, trajectories must … Read more

    Exact SDP relaxations of quadratically constrained quadratic programs with forest structures

  • Godai Azuma
  • Mituhiro Fukuda
  • Sunyoung Kim
  • Makoto Yamashita
    • Categories Global Optimization, Semi-definite Programming Tags , , ,

    We study the exactness of the semidefinite programming (SDP) relaxation of quadratically constrained quadratic programs (QCQPs). With the aggregate sparsity matrix from the data matrices of a QCQP with $n$ variables, the rank and positive semidefiniteness of the matrix are examined. We prove that if the rank of the aggregate sparsity matrix is not less … Read more

    Dual optimal design and the Christoffel-Darboux polynomial

  • Yohann De Castro
  • Didier Henrion
  • Jean-Bernard Lasserre
  • Fabrice Gamboa
    • Categories Convex Optimization, Semi-definite Programming, Statistics Tags , , ,

    The purpose of this short note is to show that the Christoffel-Darboux polynomial, useful in approximation theory and data science, arises naturally when deriving the dual to the problem of semi-algebraic D-optimal experimental design in statistics. It uses only elementary notions of convex analysis. ArticleDownload View PDF

    Stochastic Multi-level Composition Optimization Algorithms with Level-Independent Convergence Rates

  • Krishnakumar Balasubramanian
  • Saeed Ghadimi
  • Anthony Nguyen
    • Categories Nonlinear Optimization, Statistics, Stochastic Programming Tags , , ,

    In this paper, we study smooth stochastic multi-level composition optimization problems, where the objective function is a nested composition of $T$ functions. We assume access to noisy evaluations of the functions and their gradients, through a stochastic first-order oracle. For solving this class of problems, we propose two algorithms using moving-average stochastic estimates, and analyze … Read more

    An improved randomized algorithm with noise level tuning for large-scale noisy unconstrained DFO problems

  • Morteza Kimiaei
    • Categories Optimization Software Benchmark, Stochastic Programming, Unconstrained Optimization Tags , , , ,

    In this paper, a new randomized solver (called VRDFON) for noisy unconstrained derivative-free optimization (DFO) problems is discussed. Complexity result in the presence of noise for nonconvex functions is studied. Two effective ingredients of VRDFON are an improved derivative-free line search algorithm with many heuristic enhancements and quadratic models in adaptively determined subspaces. Numerical results … Read more

    A Unified Approach to Solve Convex Hull Pricing and Average Incremental Cost Pricing

  • Yonghong Chen
  • Pete Whitman
  • Richard O'Neill
    • Categories Applications - OR and Management Sciences Tags , , , , ,

    This paper introduces a unified approach to solving convex hull pricing (CHP) and average incremental cost (AIC) pricing problems. By developing a convex hull and convex envelope formulation for individual resources, a CHP model that minimizes uplift can be solved by linear programming (LP) using relaxation of the binary terms of the security constrained unit … Read more

    Optimal Residential Users Coordination Via Demand Response: An Exact Distributed Framework

  • Natalia Alguacil Conde
  • Michael David de Souza Dutra
    • Categories (Mixed) Integer Linear Programming, Energy Tags , , ,

    This paper proposes a two-phase optimization framework for users that are involved in demand response programs. In a first phase, responsive users optimize their own household consumption, characterizing not only their appliances and equipment but also their comfort preferences. Subsequently, the aggregator exploits in a second phase this preliminary noncoordinated solution by implementing a coordination … Read more

    A Column Generation Based Heuristic for the Split Delivery Vehicle Routing Problem with Time Windows

  • Pedro Munari
  • Martin Savelsbergh
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Integer Programming

    The vehicle routing problem with time windows (VRPTW) is one of the most studied variants of routing problems. We consider the Split Delivery VRPTW (SDVRPTW), an extension in which customers can be visited multiple times, if advantageous. While this additional flexibility can result in significant cost reductions, it also results in additional modeling and computational … Read more

    On complexity and convergence of high-order coordinate descent algorithms

  • V. S. Amaral
  • Roberto Andreani
  • Ernesto G. Birgin
  • José Mario Martínez
  • Diaulas S. Marcondes
    • Categories Bound-constrained Optimization, Nonlinear Optimization Tags , ,

    Coordinate descent methods with high-order regularized models for box-constrained minimization are introduced. High-order stationarity asymptotic convergence and first-order stationarity worst-case evaluation complexity bounds are established. The computer work that is necessary for obtaining first-order $\varepsilon$-stationarity with respect to the variables of each coordinate-descent block is $O(\varepsilon^{-(p+1)/p})$ whereas the computer work for getting first-order $\varepsilon$-stationarity with … Read more