Margherita Porcelli

An extrapolated and provably convergent algorithm for nonlinear matrix decomposition with the ReLU function

  • Nicolas Gillis
  • Margherita Porcelli
  • Giovanni Seraghiti
    • Categories Data Science Algorithms, Optimization in Data Science, Other Topics Tags , ,

    Nonlinear matrix decomposition (NMD) with the ReLU function, denoted ReLU-NMD, is the following problem: given a sparse, nonnegative matrix \(X\) and a factorization rank \(r\), identify a rank-\(r\) matrix \(\Theta\) such that \(X\approx \max(0,\Theta)\). This decomposition finds application in data compression, matrix completion with entries missing not at random, and manifold learning. The standard ReLU-NMD … Read more

    prunAdag: an adaptive pruning-aware gradient method

  • Margherita Porcelli
  • Giovanni Seraghiti
  • Philippe L. Toint
    • Categories Data Science Algorithms, Nonlinear Optimization Tags , , ,

    A pruning-aware adaptive gradient method is proposed which classifies the variables in two sets before updating them using different strategies. This technique extends the “relevant/irrelevant” approach of Ding (2019) and Zimmer et al. (2022) and allows a posteriori sparsification of the solution of model parameter fitting problems. The new method is proved to be convergent … Read more

    A multilevel stochastic regularized first-order method with application to training

  • Margherita Porcelli
  • Elisa Riccietti
  • Filippo Marini
    • Categories Nonlinear Optimization, Stochastic Programming

    In this paper, we propose a new multilevel stochastic framework for the solution of optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical description of the problem, being either in the classical variable space or in the function space, meaning that different levels of accuracy for the objective function … Read more

    Black-box optimization for the design of a jet plate for impingement cooling

  • Filippo Marini
  • Margherita Porcelli
  • Elisa Riccietti
  • Lorenzo Cocchi
    • Categories Applications - Science and Engineering, Optimization of Simulated Systems, Other Topics Tags , , ,

    In this work, we propose a novel black-box formulation of the impingement cooling system for a nozzle in a gas turbine. Leveraging on a well-known model that correlates the design features of the cooling system with the efficiency parameters, we develop NOZZLE, a new constrained black-box optimization formulation for the jet impingement cooling design. Then … Read more

    Regularized methods via cubic subspace minimization for nonconvex optimization

  • Stefania Bellavia
  • Davide Palitta
  • Margherita Porcelli
  • Valeria Simoncini
    • Categories Nonlinear Optimization, Unconstrained Optimization

    The main computational cost per iteration of adaptive cubic regularization methods for solving large-scale nonconvex problems is the computation of the step \(s_k\), which requires an approximate minimizer of the cubic model. We propose a new approach in which this minimizer is sought in a low dimensional subspace that, in contrast to classical approaches, is … Read more

    A semidefinite programming approach for the projection onto the cone of negative semidefinite symmetric tensors with applications to solid mechanics

  • Cristina Padovani
  • Margherita Porcelli
    • Categories Civil and Environmental Engineering, Linear, Cone and Semidefinite Programming Tags , , ,

    We propose an algorithm for computing the projection of a symmetric second-order tensor onto the cone of negative semidefinite symmetric tensors with respect to the inner product defined by an assigned positive definite symmetric fourth-order tensor C. The projection problem is written as a semidefinite programming problem and an algorithm based on a primal-dual path-following … Read more

    An Improved Penalty Algorithm using Model Order Reduction for MIPDECO problems with partial observations

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

    This work addresses optimal control problems governed by a linear time-dependent partial differential equation (PDE) as well as integer constraints on the control. Moreover, partial observations are assumed in the objective function. The resulting problem poses several numerical challenges due to the mixture of combinatorial aspects, induced by integer variables, and large scale linear algebra … Read more

    A spectral PALM algorithm for matrix and tensor-train based Dictionary Learning

  • Domitilla Brandoni
  • Margherita Porcelli
  • Valeria Simoncini
    • Categories Constrained Nonlinear Optimization Tags , , , , ,

    Dictionary Learning (DL) is one of the leading sparsity promoting techniques in the context of image classification, where the “dictionary” matrix D of images and the sparse matrix X are determined so as to represent a redundant image dataset. The resulting constrained optimization problem is nonconvex and non-smooth, providing several computational challenges for its solution. … Read more

    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