Month: February 2020

Solving Binary-Constrained Mixed Complementarity Problems Using Continuous Reformulations

  • Steven A. Gabriel
  • Martin Schmidt
  • Marina Leal
    • Categories (Mixed) Integer Nonlinear Programming, Complementarity and Variational Inequalities, Transportation Tags , , ,

    Mixed complementarity problems are of great importance in practice since they appear in various fields of applications like energy markets, optimal stopping, or traffic equilibrium problems. However, they are also very challenging due to their inherent, nonconvex structure. In addition, recent applications require the incorporation of integrality constraints. Since complementarity problems often model some kind … Read more

    A Hybrid Gradient Method for Strictly Convex Quadratic Programming

  • Oscar S. Dalmau
  • Rafael Herrera
  • Harry Oviedo
    • Categories Convex Optimization, Nonlinear Optimization, Unconstrained Optimization Tags ,

    In this paper, a reliable hybrid algorithm for solving convex quadratic minimization problems is presented. At each iteration, two points are computed: first, an auxiliary point $\dot{x}_k$ is generated by performing a gradient step equipped with an optimal steplength, then, the next iterate $x_{k+1}$ is obtained through a weighted sum of $\dot{x}_k$ with the penultimate … Read more

    Evaluating on-demand warehousing via dynamic facility location models

  • Kaan Unnu
  • Jennifer Pazour
    • Categories (Mixed) Integer Linear Programming, Supply Chain Management, Transportation Tags , , , , , ,

    On-demand warehousing platforms match companies with underutilized warehouse and distribution capabilities with customers who need extra space or distribution services. These new business models have unique advantages, in terms of reduced capacity and commitment granularity, but also have different cost structures compared to traditional ways of obtaining distribution capabilities. This research is the first quantitative … Read more

    Sum theorems for maximal monotone operators under weak compactness conditions

  • M.D. Voisei
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , ,

    This note presents a summary of our most recent results concerning the maximal monotonicity of the sum of two maximal monotone operators defined in a locally convex space under the classical interiority qualification condition when one of their domains or ranges has a weak relative compactness property. Citation NA Article Download View Sum theorems for … Read more

    Mixed-Integer Optimal Control Problems with switching costs: A shortest path approach

  • Felix Bestehorn
  • Christoph Hansknecht
  • Christian Kirches
  • Paul Manns
    • Categories (Mixed) Integer Nonlinear Programming, Approximation Algorithms Tags , , , ,

    We investigate an extension of Mixed-Integer Optimal Control Problems (MIOCPs) by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, consisting of solving a partial outer convexification to obtain a relaxed solution and using rounding schemes to obtain a discrete-valued control can still be applied, but the … Read more

    Computational study of a branching algorithm for the maximum k-cut problem

  • Miguel F. Anjos
  • Sébastien Le Digabel
  • Vilmar Jefté Rodrigues de Sousa
    • Categories Branch and Cut Algorithms, Graphs and Matroids, Semi-definite Programming Tags , , , ,

    This work considers the graph partitioning problem known as maximum k-cut. It focuses on investigating features of a branch-and-bound method to efficiently obtain global solutions. An exhaustive experimental study is carried out for two main components of a branch-and-bound algorithm: computing bounds and branching strategies. In particular, we propose the use of a variable neighborhood … Read more

    Solving Mixed-Integer Nonlinear Optimization Problems using Simultaneous Convexification – a Case Study for Gas Networks

  • Frauke Liers
  • Maximilian Merkert
  • Alexander Martin
  • Nick Mertens
  • Dennis Michaels
    • Categories Applications - Science and Engineering, Global Optimization, Network Optimization Tags , , ,

    Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations of the feasible set. Known solution approaches based on spatial branch-and-bound become more effective the tighter the used relaxations are. Relaxations are commonly established by convex underestimators, where each … Read more

    On the propagation of quality requirements for mechanical assemblies in industrial manufacturing

  • Philipp Armbrust
  • Paul Alexandru Bucur
  • Philipp Hungerländer
    • Categories Mechanical Engineering Tags , , , ,

    A frequent challenge encountered by manufacturers of mechanical assemblies consists of the definition of quality criteria for the assembly lines of the subcomponents which are mounted into the final product. The rollout of Industry 4.0 standards paves the way for the usage of data-driven, intelligent approaches towards this goal. In this work, we investigate such … Read more

    Learning Generalized Strong Branching for Set Covering, Set Packing, and 0-1 Knapsack Problems

  • Yu Yang
  • Natashia Boland
  • Bistra Dilkina
  • Martin Savelsbergh
    • Categories (Mixed) Integer Linear Programming, Integer Programming Tags , ,

    Branching on a set of variables, rather than on a single variable, can give tighter bounds at the child nodes and can result in smaller search trees. However, selecting a good set of variables to branch on is even more challenging than selecting a good single variable to branch on. Generalized strong branching extends the … Read more

    Coordinate Descent Without Coordinates: Tangent Subspace Descent on Riemannian Manifolds

  • David H. Gutman
  • Nam Ho-Nguyen
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , ,

    We extend coordinate descent to manifold domains, and provide convergence analyses for geodesically convex and non-convex smooth objective functions. Our key insight is to draw an analogy between coordinate blocks in Euclidean space and tangent subspaces of a manifold. Hence, our method is called tangent subspace descent (TSD). The core principle behind ensuring convergence of … Read more