Margherita Porcelli

Solving nonlinear systems of equations via spectral residual methods: stepsize selection and applications

  • Enrico Meli
  • Benedetta Morini
  • Margherita Porcelli
  • Cristina Sgattoni
    • Categories Mechanical Engineering, Nonlinear Systems and Least-Squares

    Spectral residual methods are derivative-free and low-cost per iteration procedures for solving nonlinear systems of equations. They are generally coupled with a nonmonotone linesearch strategy and compare well with Newton-based methods for large nonlinear systems and sequences of nonlinear systems. The residual vector is used as the search direction and choosing the steplength has a … Read more

    Exploiting problem structure in derivative free optimization

  • Margherita Porcelli
  • Philippe L. Toint
    • Categories Nonlinear Optimization, Optimization Software and Modeling Systems Tags , , ,

    A structured version of derivative-free random pattern search optimization algorithms is introduced which is able to exploit coordinate partially separable structure (typically associated with sparsity) often present in unconstrained and bound-constrained optimization problems. This technique improves performance by orders of magnitude and makes it possible to solve large problems that otherwise are totally intractable by … Read more

    A relaxed interior point method for low-rank semidefinite programming problems with applications to matrix completion

  • Stefania Bellavia
  • Jacek Gondzio
  • Margherita Porcelli
    • Categories Nonlinear Systems and Least-Squares, Semi-definite Programming Tags , , ,

    A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal solution, a special nearly low-rank form of all primal iterates is imposed. To accommodate such a (restrictive) … Read more

    Improved Penalty Algorithm for Mixed Integer PDE Constrained Optimization (MIPDECO) Problems

  • Dominik Garmatter
  • Margherita Porcelli
  • Francesco Rinaldi
  • Martin Stoll
    • Categories (Mixed) Integer Nonlinear Programming, Control Applications, Optimization of Systems modeled by PDEs Tags , , ,

    Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized PDEs. So far, the Branch-and-Bound framework has been the most common solution strategy for such problems. In order to provide an alternative solution approach, especially … Read more

    Interior Point Methods and Preconditioning for PDE-Constrained Optimization Problems Involving Sparsity Terms

  • John W. Pearson
  • Margherita Porcelli
  • Martin Stoll
    • Categories Control Applications, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , , ,

    PDE-constrained optimization problems with control or state constraints are challenging from an analytical as well as numerical perspective. The combination of these constraints with a sparsity-promoting L1 term within the objective function requires sophisticated optimization methods. We propose the use of an Interior Point scheme applied to a smoothed reformulation of the discretized problem, and … Read more

    FINITE ELEMENT MODEL UPDATING FOR STRUCTURAL APPLICATIONS

  • Maria Girardi
  • Margherita Porcelli
  • Cristina Padovani
  • Daniele Pellegrini
  • Leonardo Robol
    • Categories Civil and Environmental Engineering, Nonlinear Optimization Tags , , , ,

    A novel method for performing model updating on finite element models is presented. The approach is particularly tailored to modal analyses of buildings, by which the lowest frequencies, obtained by using sensors and system identification approaches, need to be matched to the numerical ones predicted by the model. This is done by optimizing some unknown … Read more

    A note on using performance and data profiles for training algorithms

  • Margherita Porcelli
  • Philippe L. Toint
    • Categories Nonlinear Optimization, Optimization of Simulated Systems, Optimization Software Benchmark Tags , , ,

    It is shown how to use the performance and data profile benchmarking tools to improve algorithms’ performance. An illustration for the BFO derivative-free optimizer suggests that the obtained gains are potentially significant. CitationACM Transactions on Mathematical Software, 45:2 (2019), Article 20.ArticleDownload View PDF

    Quasi-Newton methods for constrained nonlinear systems: complexity analysis and application

  • Leopoldo Marini
  • Benedetta Morini
  • Margherita Porcelli
    • Categories Nonlinear Optimization, Nonlinear Systems and Least-Squares

    We address the solution of convex constrained nonlinear systems by new linesearch Quasi-Newton methods. These methods are based on a proper use of the projection map onto the constraint set and on a derivative-free and nonmonotone linesearch strategy. The convergence properties of the proposed methods are presented along with a worst-case iteration complexity bound. Several … Read more

    Preconditioning PDE-constrained optimization with L^1-sparsity and control constraints

  • Margherita Porcelli
  • Valeria Simoncini
  • Martin Stoll
    • Categories Control Applications, Systems governed by Differential Equations Optimization Tags , , , , ,

    PDE-constrained optimization aims at finding optimal setups for partial differential equations so that relevant quantities are minimized. Including sparsity promoting terms in the formulation of such problems results in more practically relevant computed controls but adds more challenges to the numerical solution of these problems. The needed L^1-terms as well as additional inclusion of box … Read more

    Approximate norm descent methods for constrained nonlinear systems

  • Benedetta Morini
  • Margherita Porcelli
  • Philippe L. Toint
    • Categories Bound-constrained Optimization, Nonlinear Systems and Least-Squares Tags , , ,

    We address the solution of convex-constrained nonlinear systems of equations where the Jacobian matrix is unavailable or its computation/storage is burdensome. In order to efficiently solve such problems, we propose a new class of algorithms which are “derivative-free” both in the computation of the search direction and in the selection of the steplength. Search directions … Read more