globalization

A homotopy for the reliable estimation of model parameters in chromatography processes

  • Dominik H. Cebulla
  • Christian Kirches
  • Andreas Potschka
    • Categories Chemical Engineering, Nonlinear Systems and Least-Squares, Optimization of Systems modeled by PDEs Tags , , ,

    Mathematical modeling, simulation, and optimization can significantly support the development and characterization of chromatography steps in the biopharmaceutical industry. Particularly mechanistic models become preferably used, as these models, once carefully calibrated, can be employed for a reliable optimization. However, model calibration is a difficult task in this context due to high correlations between parameters, highly … Read more

    A Unified Funnel Restoration SQP Algorithm

  • David Kiessling
  • Sven Leyffer
  • Charlie Vanaret
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of four algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been implemented in the open-source solver Uno, a Swiss-army knife-like C++ optimization framework that unifies many nonlinearly constrained nonconvex optimization solvers. We illustrate the framework with … Read more

    A lower bound on the iterative complexity of the Harker and Pang globalization technique of the Newton-min algorithm for solving the linear complementarity problem

  • Jean-Pierre Dussault
  • Mathieu Frappier
  • Jean Charles Gilbert
    • Categories Complementarity and Variational Inequalities, Nonsmooth Optimization Tags , , , , , , , , ,

    The plain Newton-min algorithm for solving the linear complementarity problem (LCP) 0 ≤ x ⊥ (Mx+q) ≥ 0 can be viewed as an instance of the plain semismooth Newton method on the equational version min(x,Mx+q) = 0 of the problem. This algorithm converges for any q when M is an M-matrix, but not when it … Read more

    Backward Step Control for Global Newton-type Methods

  • Andreas Potschka
    • Categories Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , ,

    We present and analyze a new damping approach called backward step control for the globalization of the convergence of Newton-type methods for the numerical solution of nonlinear root-finding problems. We provide and discuss reasonable assumptions that imply convergence of backward step control on the basis of generalized Newton paths in conjunction with a backward analysis … Read more

    Preconditioning and Globalizing Conjugate Gradients in Dual Space for Quadratically Penalized Nonlinear-Least Squares Problems

  • Serge Gratton
  • Philippe L. Toint
  • Selime Gürol
    • Categories Nonlinear Systems and Least-Squares, Optimization of Simulated Systems, Optimization of Systems modeled by PDEs Tags , , , , ,

    When solving nonlinear least-squares problems, it is often useful to regularize the problem using a quadratic term, a practice which is especially common in applications arising in inverse calculations. A solution method derived from a trust-region Gauss-Newton algorithm is analyzed for such applications, where, contrary to the standard algorithm, the least-squares subproblem solved at each … Read more