Stefan Ulbrich

Global optimization of mixed-integer ODE constrained network problems using the example of stationary gas transport

  • Oliver Habeck
  • Marc E. Pfetsch
  • Stefan Ulbrich
    • Categories Global Optimization Tags , , ,

    In this paper we propose a new approach for finding global solutions of mixed-integer nonlinear optimization problems with ordinary differential equation constraints on networks. Instead of using a first discretize then optimize approach, we combine spatial and variable branching with appropriate discretizations of the differential equations to derive relaxations of the original problem. To construct … Read more

    A Framework for Solving Mixed-Integer Semidefinite Programs

  • Tristan Gally
  • Marc E. Pfetsch
  • Stefan Ulbrich
    • Categories (Mixed) Integer Nonlinear Programming, Optimization Software and Modeling Systems, Semi-definite Programming

    Mixed-integer semidefinite programs arise in many applications and several problem-specific solution approaches have been studied recently. In this paper, we investigate a generic branch-and-bound framework for solving such problems. We first show that strict duality of the semidefinite relaxations is inherited to the subproblems. Then solver components like dual fixing, branching rules, and primal heuristics … Read more

    A globally convergent primal-dual interior-point filter method for nonlinear programming: new filter optimality measures and computational results

  • R. Silva
  • Michael Ulbrich
  • Stefan Ulbrich
  • Luis Nunes Vicente
    • Categories Constrained Nonlinear Optimization, Optimization Software and Modeling Systems, Quadratic Programming Tags , , , ,

    In this paper we modify the original primal-dual interior-point filter method proposed in [18] for the solution of nonlinear programming problems. We introduce two new optimality filter entries based on the objective function, and thus better suited for the purposes of minimization, and propose conditions for using inexact Hessians. We show that the global convergence … Read more

    Primal-dual interior point methods for PDE-constrained optimization

  • Michael Ulbrich
  • Stefan Ulbrich
    • Categories Constrained Nonlinear Optimization, Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization Tags , , , , ,

    This paper provides a detailed analysis of a primal-dual interior-point method for PDE-constrained optimization. Considered are optimal control problems with control constraints in $L^p$. It is shown that the developed primal-dual interior-point method converges globally and locally superlinearly. Not only the easier $L^\infty$-setting is analyzed, but also a more involved $L^q$-analysis, $q

    On the superlinear local convergence of a filter-SQP method

  • Stefan Ulbrich
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    Transition to superlinear local convergence is shown for a modified version of the trust-region filter-SQP method for nonlinear programming introduced by Fletcher, Leyffer, and Toint [8]. Hereby, the original trust-region SQP-steps can be used without an additional second order correction. The main modification consists in using the Lagrangian function value instead of the objective function … Read more

    A globally convergent primal-dual interior-point filter method for nonlinear programming

  • Michael Ulbrich
  • Stefan Ulbrich
  • Luis Nunes Vicente
    • Categories Nonlinear Optimization Tags , , ,

    In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primal-dual interior-point algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primal-dual step obtained from the perturbed first-order necessary conditions into a normal and a tangential step, … Read more