Martin Neuenhofen

Dynamic Optimization with Convergence Guarantees

  • Eric C. Kerrigan
  • Martin Neuenhofen
    • Categories Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization

    We present a novel direct transcription method to solve optimization problems subject to nonlinear differential and inequality constraints. In order to provide numerical convergence guarantees, it is sufficient for the functions that define the problem to satisfy boundedness and Lipschitz conditions. Our assumptions are the most general to date; we do not require uniqueness, differentiability … Read more

    Significant Generalization of the Convergence Proof for the Direct Transcription Method for Constrained Optimal Control Problems

  • Martin Neuenhofen
    • Categories Nonlinear Optimization

    In the arXiv paper [arXiv:1712.07761] from December 2017 we presented a convergent direct transcription method for optimal control problems. In the present paper we present a significantly generalized convergence theory in succinct form. Therein, we replace strong assumptions that we had formerly made on local uniqueness of the solution, and on differentiability of a particular … Read more

    Stable interior point method for convex quadratic programming with strict error bounds

  • Stefania Bellavia
  • Martin Neuenhofen
    • Categories Quadratic Programming Tags , , ,

    We present a short step interior point method for solving a class of nonlinear programming problems with quadratic objective function. Convex quadratic programming problems can be reformulated as problems in this class. The method is shown to have weak polynomial time complexity. A complete proof of the numerical stability of the method is provided. No … Read more