On the paper “Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem”

  • Luís Felipe Bueno
  • Gabriel Haeser
  • Oliver Kolossoski
    • Categories Nonlinear Optimization Tags , ,

    In the paper [Torrealba, E.M.R. et al. Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem. EJOR, 299(1) 46–59, 2021] an augmented Lagrangian algorithm was proposed for resource allocation problems with the intriguing characteristic that instead of solving the box-constrained augmented Lagrangian subproblem, they propose projecting the solution of the unconstrained subproblem onto … Read more

    A classification method based on a cloud of spheres

  • Tiago Dias
  • Paula Alexandra Amaral
    • Categories (Mixed) Integer Nonlinear Programming, Data Science Algorithms, Quadratic Programming Tags , , ,

    \(\) In this article we propose a binary classification model to distinguish a specific class that corresponds to a characteristic that we intend to identify (fraud, spam, disease). The classification model is based on a cloud of spheres that circumscribes the points of the class to be identified. It is intended to build a model … Read more

    Enhancements of Discretization Approaches for Non-Convex Mixed-Integer Quadratically Constraint Quadratic Programming: Part II

  • Ben Beach
  • Robert Burlacu
  • Andreas Bärmann
  • Lukas Hager
  • Robert Hildebrand
    • Categories (Mixed) Integer Nonlinear Programming, Nonlinear Optimization, Quadratic Programming Tags , , , ,

    Abstract. This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for non-convex continuous variable products and extend the well-known MIP relaxation normalized multiparametric disaggregation technique (NMDT), applying a sophisticated discretization to both … Read more

    Toward Efficient Transportation Electrification of Heavy-Duty Trucks: Joint Scheduling of Truck Routing and Charging

  • Mikhail Bragin
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization, Transportation Tags

    The timely transportation of goods to customers is an essential component of economic activities. However, heavy-duty diesel trucks that deliver goods contribute significantly to greenhouse gas emissions within many large metropolitan areas, including Los Angeles, New York, and San Francisco. To facilitate freight electrification, this paper proposes joint routing and charging (JRC) scheduling for electric … Read more

    Semi-Infinite Mixed Binary and Disjunctive Programs: Applications to Set-Covering with Infinite Demand Points and Implicit Hitting Set Problems

  • Manish Bansal
    • Categories Combinatorial Optimization, Integer Programming, Semi-infinite Programming

    Sherali and Adams [Discrete Applied Math. 157: 1319-1333, 2009] derived convex hull of semi-infinite mixed binary linear programs (SIMBLPs) using Reformulation-Linearization Technique (RLT). In this paper, we study semi-infinite disjunctive programs (SIDPs — a generalization of SIMBLPs) and present linear programming equivalent and valid inequalities for them. We utilize these results for deriving a hierarchy … Read more

    Semi-Infinite Generalized Disjunctive and Mixed Integer Convex Programs with(out) Uncertainty

  • Manish Bansal
    • Categories 0-1 Programming, Convex Optimization, Semi-infinite Programming

    In this paper, we introduce semi-infinite generalized disjunctive programs that are defined by logical propositions along with disjunctions of sets of logical equations and infinite number of algebraic inequalities. We denote these programs by SIGDPs. For SIGDPs with linear and convex inequalities, we present new reformulations: semi-infinite mixed-binary/disjunctive linear programs and semi-infinite mixed-binary/disjunctive convex programs, … Read more

    Recognizing Series-Parallel Matrices in Linear Time

  • Matthias Walter
    • Categories Graphs and Matroids Tags ,

    \(\) A series-parallel matrix is a binary matrix that can be obtained from an empty matrix by successively adjoining rows or columns that are copies of an existing row/column or have at most one 1-entry. Equivalently, series-parallel matrices are representation matrices of graphic matroids of series-parallel graphs, which can be recognized in linear time. We … Read more

    ALSO-X#: Better Convex Approximations for Distributionally Robust Chance Constrained Programs

  • Nan Jiang
  • Weijun Xie
    • Categories Stochastic Programming Tags , , ,

    This paper studies distributionally robust chance constrained programs (DRCCPs), where the uncertain constraints must be satisfied with at least a probability of a prespecified threshold for all probability distributions from the Wasserstein ambiguity set. As DRCCPs are often nonconvex and challenging to solve optimally, researchers have been developing various convex inner approximations. Recently, ALSO-X has … Read more

    Fair and Risk-averse Urban Air Mobility Resource Allocation Under Uncertainties

  • Luying Sun
  • Weijun Xie
    • Categories Applications - OR and Management Sciences Tags , , , ,

    Urban Air Mobility (UAM) is an emerging air transportation mode to alleviate the ground traffic burden and achieve zero direct aviation emissions. Due to the potential economic scaling effects, the UAM traffic flow is expected to increase dramatically once implemented, and its market can be substantially large. To be prepared for the era of UAM, … Read more

    Recovering Dantzig-Wolfe Bounds by Cutting Planes

  • Rui Chen
  • Oktay Gunluk
  • Andrea Lodi
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches Tags , ,

    Dantzig-Wolfe (DW) decomposition is a well-known technique in mixed-integer programming (MIP) for decomposing and convexifying constraints to obtain potentially strong dual bounds. We investigate cutting planes that can be derived using the DW decomposition algorithm and show that these cuts can provide the same dual bounds as DW decomposition. More precisely, we generate one cut … Read more