Applications – Science and Engineering

A BFGS-SQP Method for Nonsmooth, Nonconvex, Constrained Optimization and its Evaluation using Relative Minimization Profiles

  • Frank E. Curtis
  • Tim Mitchell
  • Michael L. Overton
    • Categories Control Applications, Nonsmooth Optimization, Optimization Software Benchmark

    We propose an algorithm for solving nonsmooth, nonconvex, constrained optimization problems as well as a new set of visualization tools for comparing the performance of optimization algorithms. Our algorithm is a sequential quadratic optimization method that employs Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton Hessian approximations and an exact penalty function whose parameter is controlled using a steering strategy. … Read more

    Second-Order Cone Programming for P-Spline Simulation Metamodeling

  • Farid Alizadeh
  • Yu Xia
    • Categories Optimization of Simulated Systems, Second-Order Cone Programming, Statistics Tags , ,

    This paper approximates simulation models by B-splines with a penalty on high-order finite differences of the coefficients of adjacent B-splines. The penalty prevents overfitting. The simulation output is assumed to be nonnegative. The nonnegative spline simulation metamodel is casted as a second-order cone programming model, which can be solved efficiently by modern optimization techniques. The … Read more

    A Distributionally-robust Approach for Finding Support Vector Machines

  • Changhyeok Lee
  • Sanjay Mehrotra
    • Categories Data-Mining, Robust Optimization, Stochastic Programming Tags , , , ,

    The classical SVM is an optimization problem minimizing the hinge losses of mis-classified samples with the regularization term. When the sample size is small or data has noise, it is possible that the classifier obtained with training data may not generalize well to pop- ulation, since the samples may not accurately represent the true population … Read more

    An efficient second-order cone programming approach for optimal selection in tree breeding

  • Tim J. Mullin
  • Sena Safarina
  • Makoto Yamashita
    • Categories Applications - Science and Engineering, Second-Order Cone Programming Tags , , , , , ,

    An important problem in tree breeding is optimal selection from candidate pedigree members to produce the highest performance in seed orchards, while conserving essential genetic diversity. The most beneficial members should contribute as much as possible, but such selection of orchard parents would reduce performance of the orchard progeny due to serious inbreeding. To avoid … Read more

    A Stochastic Optimization Model for Designing Last Mile Relief Networks

  • Semih Atakan
  • Nilay Noyan
  • Burcu Balcik
    • Categories Applications - Science and Engineering, Stochastic Programming

    In this study, we introduce a distribution network design problem that determines the locations and capacities of the relief distribution points in the last mile network, while considering demand- and network-related uncertainties in the post-disaster environment. The problem addresses the critical concerns of relief organizations in designing last mile networks, which are providing accessible and … Read more

    Minimum cost Layout Decomposition and Legalization for Triple Patterning Lithography

  • Xingquan Li
  • Wenxing Zhu
  • Ziran Zhu
    • Categories VLSI layout

    With the need of 16/11nm cells, triple patterning lithography (TPL) has been concerned in lithography industry. Based on a new conflict projection technique to identify conflicts, we formulate in this paper the TPL layout decomposition problem as a minimum cost coloring problem. The problem is solved in two steps. First, it is relaxed to a … Read more

    A Polyhedral Study of the Integrated Minimum-Up/-Down Time and Ramping Polytope

  • Yongpei Guan
  • Kai Pan
    • Categories Applications - Science and Engineering, Cutting Plane Approaches

    In this paper, we consider the polyhedral structure of the integrated minimum-up/-down time and ramping polytope for the unit commitment problem. Our studied generalized polytope includes minimum-up/-down time constraints, generation ramp-up/-down rate constraints, logical constraints, and generation upper/lower bound constraints. We derive strong valid inequalities by utilizing the structures of the unit commitment problem, and … Read more

    Regularization vs. Relaxation: A convexification perspective of statistical variable selection

  • Kun Chen
  • Hongbo Dong
  • Jeff Linderoth
    • Categories (Mixed) Integer Nonlinear Programming, Linear, Cone and Semidefinite Programming, Statistics Tags , , ,

    Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a quadratic optimization problem with an $\ell_0$-norm penalty. Exactly enforcing the $\ell_0$-norm penalty is computationally intractable for larger scale problems, so different sparsity-inducing penalty … Read more

    A New Perspective on Boosting in Linear Regression via Subgradient Optimization and Relatives

  • Robert M. Freund
  • Rahul Mazumder
  • Paul Grigas
    • Categories Data-Mining, Nonsmooth Optimization, Statistics Tags , , , ,

    In this paper we analyze boosting algorithms in linear regression from a new perspective: that of modern first-order methods in convex optimization. We show that classic boosting algorithms in linear regression, namely the incremental forward stagewise algorithm (FS-epsilon) and least squares boosting (LS-Boost-epsilon), can be viewed as subgradient descent to minimize the loss function defined … Read more

    Strong SOCP Relaxations for the Optimal Power Flow Problem

  • Santanu S. Dey
  • Burak Kocuk
  • Xu Andy Sun
    • Categories Applications - Science and Engineering, Global Optimization, Nonlinear Optimization Tags , , ,

    This paper proposes three strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem. These three relaxations are incomparable to each other and two of them are incomparable to the standard SDP relaxation of OPF. Extensive computational experiments show that these relaxations have numerous advantages over existing convex relaxations in … Read more