A Gauss-Newton approach for solving constrained optimization problems using differentiable exact penalties

  • Roberto Andreani
  • Ellen H. Fukuda
  • Paulo J. S. Silva
    • Categories Constrained Nonlinear Optimization Tags , , ,

    We propose a Gauss-Newton-type method for nonlinear constrained optimization using the exact penalty introduced recently by Andre and Silva for variational inequalities. We extend their penalty function to both equality and inequality constraints using a weak regularity assumption, and as a result, we obtain a continuously differentiable exact penalty function and a new reformulation of … Read more

    Experiments with a Generic Dantzig-Wolfe Decomposition for Integer Programs

  • Gerald Gamrath
  • Marco E. Lübbecke
    • Categories (Mixed) Integer Linear Programming Tags , , ,

    We report on experiments with turning the branch-cut-and-price framework SCIP into a generic branch-cut-and-price solver. That is, given a mixed integer program (MIP), our code performs a Dantzig-Wolfe decomposition according to the user’s specification, and solves the resulting re-formulation via branch-and-price. We take care of the column generation subproblems which are solved as MIPs themselves, … Read more

    Estimating Computational Noise

  • Jorge Moré
  • Stefan M. Wild
    • Categories Nonlinear Optimization, Optimization Software and Modeling Systems, Other Topics Tags , ,

    Computational noise in deterministic simulations is as ill-defined a concept as can be found in scientific computing. When coupled with adaptive strategies, the effects of finite precision destroy smoothness of the simulation output and complicate subsequent analysis. Following the work of Hamming on roundoff errors, we present a new algorithm, ECnoise, for quantifying the noise … Read more

    A branch-and-price algorithm for multi-mode resource leveling

  • Eamonn T. Coughlan
  • Marco E. Lübbecke
  • Jens Schulz
    • Categories (Mixed) Integer Linear Programming, Scheduling Tags , ,

    Resource leveling is a variant of resource-constrained project scheduling in which a non-regular objective function, the resource availability cost, is to be minimized. We present a branch-and-price approach together with a new heuristic to solve the more general turnaround scheduling problem. Besides precedence and resource constraints, also availability periods and multiple modes per job have … Read more

    An interior-point method for minimizing the sum of piecewise-linear convex functions

  • Toshihiro Kosaki
    • Categories Nonlinear Optimization Tags , ,

    We consider the problem to minimize the sum of piecewise-linear convex functions under both linear and nonnegative constraints. We convert the piecewise-linear convex problem into a standard form linear programming problem (LP) and apply a primal-dual interior-point method for the LP. From the solution of the converted problem, we can obtain the solution of the … Read more

    Exactly solving a Two-level Hierarchical Location Problem with modular node capacities

  • Bernardetta Addis
  • Giuliana Carello
  • Alberto Ceselli
    • Categories (Mixed) Integer Linear Programming, Telecommunications Tags , , , ,

    In many telecommunication networks a given set of client nodes must be served by different sets of facilities, providing different services and having different capabilities, which must be located and dimensioned in the design phase. Network topology must be designed as well, by assigning clients to facilities and facilities to higher level entities, when necessary. … Read more

    A MATHEMATICAL PROGRAMMING MODEL FOR THE DESIGN OF AIRPORT CONFIGURATIONS

  • Esteve Codina
  • Ángel Marín
    • Categories Airline Optimization, Transportation Tags , ,

    A mathematical programming model for assessing the design of an optimal airport topology is presented herein. It takes into account the efficient and safe taxiing of aircraft on the ground. We balance a set of conflicting factors that depend directly on aircraft trajectories on the ground, such as the number of arriving and departing flights … Read more

    An inexact interior point method for L1-regularized sparse covariance selection

  • Lu Li
  • Kim-Chuan Toh
    • Categories Convex Optimization, Semi-definite Programming, Statistics Tags , , , ,

    Sparse covariance selection problems can be formulated as log-determinant (log-det) semidefinite programming (SDP) problems with large numbers of linear constraints. Standard primal-dual interior-point methods that are based on solving the Schur complement equation would encounter severe computational bottlenecks if they are applied to solve these SDPs. In this paper, we consider a customized inexact primal-dual … Read more

    On Computation of Performance Bounds of Optimal Index Assignment

  • Hans D Mittelmann
  • Xiaolin Wu
  • J. Wang
  • X. Wang
    • Categories Applications - Science and Engineering, Semi-definite Programming Tags , , , , ,

    Channel-optimized index assignment of source codewords is arguably the simplest way of improving transmission error resilience, while keeping the source and/or channel codes intact. But optimal design of index assignment is an in- stance of quadratic assignment problem (QAP), one of the hardest optimization problems in the NP-complete class. In this paper we make a … Read more

    Minimizing irregular convex functions: Ulam stability for approximate minima

  • Emil Ernst
  • Michel Thera
    • Categories Convex Optimization Tags , , ,

    The main concern of this article is to study Ulam stability of the set of $\varepsilon$-approximate minima of a proper lower semicontinuous convex function bounded below on a real normed space $X$, when the objective function is subjected to small perturbations (in the sense of Attouch \& Wets). More precisely, we characterize the class all … Read more