homotopy methods

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 Primal-Dual Homotopy Algorithm for l_1-Minimization with l_inf-Constraints

  • Christoph Brauer
  • Dirk A. Lorenz
  • Andreas M. Tillmann
    • Categories Convex Optimization, Linear Programming Tags , , , ,

    In this paper we propose a primal-dual homotopy method for $\ell_1$-minimization problems with infinity norm constraints in the context of sparse reconstruction. The natural homotopy parameter is the value of the bound for the constraints and we show that there exists a piecewise linear solution path with finitely many break points for the primal problem … Read more

    Optimization and homotopy methods for the Gibbs free energy of magmatic mixtures

  • Andrea Cassioli
  • Luca Consolini
  • Marco Locatelli
  • Antonella Longo
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Global Optimization Applications Tags , , ,

    In this paper we consider a mathematical model for magmatic mixtures based on the Gibbs free energy. Different reformulations of the problem are presented and some theoretical results about the existence and number of solutions are derived. Finally, two homotopy methods and a global optimization one are introduced and computationally tested. One of the homotopy … Read more