Linear Programming

Application of a Gas Market Model with Linear Programming. The Influence of the Dollar Exchange Rate on the Wholesale Price of Natural Gas in Northwest Europe until 2040

  • Maik Günther
    • Categories Finance and Economics, Linear Programming, Optimization of Simulated Systems Tags , , , , , , , , ,

    The price of natural gas at wholesale markets in Northwest Europe is influenced by numerous parameters. The USD to EUR exchange rate is one of these parameters. Using the LP-based gas market model WEGA, this paper will examine the impact of USD exchange rates on wholesale natural gas prices in Northwest Europe from 2025 to … Read more

    Polyhedral Properties of RLT Relaxations of Nonconvex Quadratic Programs and Their Implications on Exact Relaxations

  • Yuzhou Qiu
  • E. Alper Yildirim
    • Categories Global Optimization, Linear Programming, Quadratic Programming Tags , , ,

    We study linear programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT), referred to as RLT relaxations. We investigate the relations between the polyhedral properties of the feasible regions of a quadratic program and its RLT relaxation. We establish various connections between recession directions, boundedness, and vertices of the two feasible regions. … Read more

    An infeasible interior-point arc-search method with Nesterov’s restarting strategy for linear programming problems

  • Einosuke Iida
  • Makoto Yamashita
    • Categories Linear Programming Tags , , ,

    An arc-search interior-point method is a type of interior-point method that approximates the central path by an ellipsoidal arc, and it can often reduce the number of iterations. In this work, to further reduce the number of iterations and the computation time for solving linear programming problems, we propose two arc-search interior-point methods using Nesterov’s … Read more

    An easily computable upper bound on the Hoffman constant for homogeneous inequality systems

  • Javier F. Peña
    • Categories Linear Programming, Polyhedra, Second-Order Cone Programming Tags , ,

    Let $A\in \mathbb{R}^{m\times n}\setminus \{0\}$ and $P:=\{x:Ax\le 0\}$. This paper provides a procedure to compute an upper bound on the following {\em homogeneous Hoffman constant} \[ H_0(A) := \sup_{u\in \mathbb{R}^n \setminus P} \frac{\text{dist}(u,P)}{\text{dist}(Au, \mathbb{R}^m_-)}. \] In sharp contrast to the intractability of computing more general Hoffman constants, the procedure described in this paper is entirely … Read more

    Orbital Crossover

  • Ethan Deakins
  • Bernard Knueven
  • James Ostrowski
    • Categories Convex Optimization, Linear Programming, Optimization Software Benchmark Tags , ,

    Symmetry in optimization has been known to wreak havoc in optimization algorithms. Often, some of the hardest instances are highly symmetric. This is not the case in linear programming, as symmetry allows one to reduce the size of the problem, possibly dramatically, while still maintaining the same optimal objective value. This is done by aggregating … Read more

    Regularized Nonsmooth Newton Algorithms for Best Approximation

  • Yair Censor
  • Walaa M. Moursi
  • Tyler Weames
  • Henry Wolkowicz
    • Categories Convex Optimization, Linear Programming, Nonsmooth Optimization Tags , , , , ,

    We consider the problem of finding the best approximation point from a polyhedral set, and its applications, in particular to solving large-scale linear programs. The classical projection problem has many various and many applications. We study a regularized nonsmooth Newton type solution method where the Jacobian is singular; and we compare the computational performance to … Read more

    A binary linear programming approach for supporting administrative territorial consolidation

  • Radu Buzatu
  • Igor Mandric
    • Categories 0-1 Programming, Combinatorial Optimization, Linear Programming Tags , , ,

    The objective of this paper is to develop a scalable binary linear programming model for finding the optimal aggregation of communes into spatially contiguous administrative territorial units (ATUs) constrained on certain balancing criteria. The requirement for the ATUs to be contiguous represents the main computational bottleneck and, therefore, it prevents one from using such models … Read more

    COIL: A Deep Architecture for Column Generation

  • Behrouz Babaki
  • Sanjay Dominik Jena
    • Categories Linear Programming Tags , , ,

    Column generation is a popular method to solve large-scale linear programs with an exponential number of variables. Several important applications, such as the vehicle routing problem, rely on this technique in order to be solved. However, in practice, column generation methods suffer from slow convergence (i.e. they require too many iterations). Stabilization techniques, which carefully … Read more

    Polynomial worst-case iteration complexity of quasi-Newton primal-dual interior point algorithms for linear programming

  • Francisco N. C. Sobral
  • Jacek Gondzio
    • Categories Linear Programming, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , ,

    Quasi-Newton methods are well known techniques for large-scale numerical optimization. They use an approximation of the Hessian in optimization problems or the Jacobian in system of nonlinear equations. In the Interior Point context, quasi-Newton algorithms compute low-rank updates of the matrix associated with the Newton systems, instead of computing it from scratch at every iteration. … Read more