Stefania Bellavia

A Levenberg-Marquardt method for large nonlinear least-squares problems with dynamic accuracy in functions and gradients

  • Stefania Bellavia
  • Serge Gratton
  • Elisa Riccietti
    • Categories Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags

    In this paper we consider large scale nonlinear least-squares problems for which function and gradient are evaluated with dynamic accuracy and propose a Levenberg-Marquardt method for solving such problems. More precisely, we consider the case in which the exact function to optimize is not available or its evaluation is computationally demanding, but ap- proximations of … Read more

    Sequential Linear Programming and Particle Swarm Optimization for the optimization of energy districts

  • Stefania Bellavia
  • Elisa Riccietti
  • Stefano Sello
    • Categories Basic Sciences Applications, Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    In this paper we deal with the optimization of energy resources management of industrial districts, with the aim of minimizing the customer energy expenses. In a district the number of possible energy system combinations is really large, and a manual design approach might lead to a suboptimal solution. For this reason we designed a software … Read more

    An inexact dual logarithmic barrier method for solving sparse semidefinite programs

  • Stefania Bellavia
  • Jacek Gondzio
  • Margherita Porcelli
    • Categories Nonlinear Optimization, Semi-definite Programming

    A dual logarithmic barrier method for solving large, sparse semidefinite programs is proposed in this paper. The method avoids any explicit use of the primal variable X and therefore is well-suited to problems with a sparse dual matrix S. It relies on inexact Newton steps in dual space which are computed by the conjugate gradient … Read more

    On an adaptive regularization for ill-posed nonlinear systems and its trust-region implementation

  • Stefania Bellavia
  • Benedetta Morini
  • Elisa Riccietti
    • Categories Nonlinear Optimization Tags , , ,

    In this paper we address the stable numerical solution of nonlinear ill-posed systems by a trust-region method. We show that an appropriate choice of the trust-region radius gives rise to a procedure that has the potential to approach a solution of the unperturbed system. This regularizing property is shown theoretically and validated numerically. CitationDipartimento di … Read more

    On the update of constraint preconditioners for regularized KKT systems

  • Stefania Bellavia
  • Valentina De Simone
  • Daniela di Serafino
  • Benedetta Morini
    • Categories Nonlinear Optimization, Quadratic Programming Tags , , ,

    We address the problem of preconditioning sequences of regularized KKT systems, such as those arising in Interior Point methods for convex quadratic programming. In this case, Constraint Preconditioners (CPs) are very effective and widely used; however, when solving large-scale problems, the computational cost for their factorization may be high, and techniques for approximating them appear … Read more

    Preconditioning issues in the numerical solution of nonlinear equations and nonlinear least squares

  • Stefania Bellavia
  • Margherita Porcelli
    • Categories Nonlinear Optimization Tags , ,

    Second order methods for optimization call for the solution of sequences of linear systems. In this survey we will discuss several issues related to the preconditioning of such sequences. Covered topics include both techniques for building updates of factorized preconditioners and quasi-Newton approaches. Sequences of unsymmetric linear systems arising in Newton- Krylov methods will be … Read more

    Updating constraint preconditioners for KKT systems in quadratic programming via low-rank corrections

  • Stefania Bellavia
  • Valentina De Simone
  • Daniela di Serafino
  • Benedetta Morini
    • Categories Quadratic Programming Tags , , , ,

    This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems. This task is the computational core of the interior point procedure and an efficient preconditioning strategy is crucial for the efficiency of the overall method. Constraint preconditioners are very effective … Read more

    Strong local convergence properties of adaptive regularized methods for nonlinear least-squares

  • Stefania Bellavia
  • Benedetta Morini
    • Categories Nonlinear Systems and Least-Squares Tags , , ,

    This paper studies adaptive regularized methods for nonlinear least-squares problems where the model of the objective function used at each iteration is either the Euclidean residual regularized by a quadratic term or the Gauss-Newton model regularized by a cubic term. For suitable choices of the regularization parameter the role of the regularization term is to … Read more

    New updates of incomplete LU factorizations and applications to large nonlinear systems

  • Stefania Bellavia
  • Benedetta Morini
  • Margherita Porcelli
    • Categories Nonlinear Optimization Tags , , , ,

    In this paper, we address the problem of preconditioning sequences of large sparse nonsymmetric systems of linear equations and present two new strategies to construct approximate updates of factorized preconditioners. Both updates are based on the availability of an incomplete LU (ILU) factorization for one matrix of the sequence and differ in the approximation of … Read more

    A preconditioning framework for sequences of diagonally modified linear systems arising in optimization

  • Stefania Bellavia
  • Valentina De Simone
  • Daniela di Serafino
  • Benedetta Morini
    • Categories Nonlinear Optimization Tags , , ,

    We propose a framework for building preconditioners for sequences of linear systems of the form $(A+\Delta_k) x_k=b_k$, where $A$ is symmetric positive semidefinite and $\Delta_k$ is diagonal positive semidefinite. Such sequences arise in several optimization methods, e.g., in affine-scaling methods for bound-constrained convex quadratic programming and bound-constrained linear least squares, as well as in trust-region … Read more