parameter estimation

A Graphical Global Optimization Framework for Parameter Estimation of Statistical Models with Nonconvex Regularization Functions

  • Danial Davarnia
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Global Optimization Theory Tags , , , ,

    Optimization problems with norm-bounding constraints appear in various applications, from portfolio optimization to machine learning, feature selection, and beyond. A widely used variant of these problems relaxes the norm-bounding constraint through Lagrangian relaxation and moves it to the objective function as a form of penalty or regularization term. A challenging class of these models uses … Read more

    From Estimation to Optimization via Shrinkage

  • Gérard Cornuéjols
  • Danial Davarnia
    • Categories Quadratic Programming, Statistics, Stochastic Programming Tags , , , ,

    We study a class of quadratic stochastic programs where the distribution of random variables has unknown parameters. A traditional approach is to estimate the parameters using a maximum likelihood estimator (MLE) and to use this as input in the optimization problem. For the unconstrained case, we show that an estimator that “shrinks” the MLE towards … Read more

    Modeling and Simulation of Metabolic Networks for Estimation of Biomass Accumulation Parameters

  • Lorenz T. Biegler
  • Bulent Karasozen
  • Metin Turkay
  • Ugur Kaplan
    • Categories Biomedical Applications, Systems governed by Differential Equations Optimization Tags , ,

    Metabolic networks are defined as the collection of biochemical reactions within a cell that define the functions of that cell. Due to the growing need to understand the functions of biological organisms for industrial and medical purposes, modeling and simulation of metabolic networks has attracted a lot of attention recently. Traditionally, metabolic networks are modeled … Read more

    Finding optimal algorithmic parameters using a mesh adaptive direct search

  • Charles Audet
  • Dominique Orban
    • Categories Nonlinear Optimization, Nonsmooth Optimization, Unconstrained Optimization Tags , , , , ,

    The objectives of this paper are twofold; we first demonstrate the flexibility of the mesh adaptive direct search (MADS) in identifying locally optimal algorithmic parameters. This is done by devising a general framework for parameter tuning. The framework makes provision for surrogate objectives. Parameters are sought so as to minimize some measure of performance of … Read more