Benedetta Morini

Adaptive Cubic Regularization methods with dynamic inexact Hessian information and applications to finite-sum minimization

  • Stefania Bellavia
  • Benedetta Morini
  • Gianmarco Gurioli
    • Categories Unconstrained Optimization Tags

    We consider the Adaptive Regularization with Cubics approach for solving nonconvex optimization problems and propose a new variant based on inexact Hessian information chosen dynamically. The theoretical analysis of the proposed procedure is given. The key property of ARC framework, constituted by optimal worst-case function/derivative evaluation bounds for first- and second-order critical point, is guaranteed. … Read more

    Stability and accuracy of Inexact Interior Point methods for convex quadratic programming

  • Benedetta Morini
  • Valeria Simoncini
    • Categories Nonlinear Optimization Tags , ,

    We consider primal-dual IP methods where the linear system arising at each iteration is formulated in the reduced (augmented) form and solved approximately. Focusing on the iterates close to a solution, we analyze the accuracy of the so-called inexact step, i.e., the step that solves the unreduced system, when combining the effects of both different … Read more

    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

    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

    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. Citation Dipartimento … Read more

    A comparison of reduced and unreduced KKT systems arising from Interior Point methods

  • Benedetta Morini
  • Valeria Simoncini
  • Mattia Tani
    • Categories Quadratic Programming Tags , , ,

    We address the iterative solution of symmetric KKT systems arising in the solution of convex quadratic programming problems. Two strictly related and well established formulations for such systems are studied with particular emphasis on the effect of preconditioning strategies on their relation. Constraint and augmented preconditioners are considered, and the choice of the augmentation Matrix … Read more

    Spectral estimates for unreduced symmetric KKT systems arising from Interior Point methods

  • Benedetta Morini
  • Valeria Simoncini
  • Mattia Tani
    • Categories Quadratic Programming Tags , , , ,

    We consider symmetrized KKT systems arising in the solution of convex quadratic programming problems in standard form by Interior Point methods. Their coefficient matrices usually have 3×3 block structure and, under suitable conditions on both the quadratic programming problem and the solution, they are nonsingular in the limit. We present new spectral estimates for these … 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

    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

    On the use of iterative methods in cubic regularization for unconstrained optimization

  • Tommaso Bianconcini
  • Giampaolo Liuzzi
  • Benedetta Morini
  • Marco Sciandrone
    • Categories Nonlinear Optimization Tags , , ,

    In this paper we consider the problem of minimizing a smooth function by using the Adaptive Cubic Regularized framework (ARC). We focus on the computation of the trial step as a suitable approximate minimizer of the cubic model and discuss the use of matrix-free iterative methods. Our approach is alternative to the implementation proposed in … Read more