SCRO / Journées de l'optimisation

HEC Montréal, 29-31 mai 2023


HEC Montréal, 29 — 31 mai 2023

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NOJI Numerical optimization and linear algebra with Julia I

29 mai 2023 10h30 – 12h10

Salle: Transat (jaune)

Présidée par Tangi Migot

4 présentations

  • 10h30 - 10h55

    Multi-Precision Quadratic Regularization for Continuous Non-Linear Optimization

    • Dominique Monnet, prés., GERAD and Polytechnique Montréal
    • Dominique Orban, GERAD - Polytechnique Montréal

    This talk introduces MPR2, a multi-precision gradient descent algorithm with adaptive step size. At each iteration, MPR2 selects among several floating point formats to evaluate the objective function and the gradient. MPR2 aims to use the lowest precision format to save computational effort while maintaining the convergence properties. We discuss some of the pitfalls arising when using low precision computations (rounding errors, overflow, etc) and what mechanisms MPR2 implements to avoid them. We finally introduce the Julia package implementing MPR2 and present numerical results.

  • 10h55 - 11h20

    Solving nonsmooth regularized optimization problems using proximal methods in Julia.

    • Geoffroy Leconte, prés., Polytechnique Montréal
    • Dominique Orban, GERAD - Polytechnique Montréal
    • Joshua Wolff, ENSTA Paris

    We describe our package RegularizedOptimization.jl that contains several proximal methods for solving nonsmooth regularized optization problems. In particular, we present TRDH (Trust-Region Diagonal Hessian), a new trust-region method based on diagonal Quasi-Newton approximations that uses a generalization of proximal operators implemented in ShiftedProximalOperators.jl. We compare TRDH to a quadratic regularization algorithm named R2, also available in RegularizedOptimization.jl. Our goal is to reduce the number of objective and gradient evaluation, and, if possible, to decrease the number of proximal evaluations. We show the performance of these solvers on optimization problems modeled in RegularizedProblems.jl. We include TRDH results with several diagonal quasi-Newton approximations (available in LinearOperators.jl), as well as results where TRDH and R2 are used as sub-problem solvers in a trust-region (TR) algorithm. Our experiments reveal that we often have a TRDH variant that is more efficient than R2.

  • 11h20 - 11h45

    JuliaHSL: the ultimate collection for large scale scientific computation

    • Alexis Montoison, prés.,
    • Dominique Orban, GERAD - Polytechnique Montréal

    HSL is a collection of state-of-the-art Fortran packages for large-scale scientific computation.
    The new package JuliaHSL, jointly developed with the Computational Mathematics Group at the STFC Rutherford Appleton Laboratory, aims to facilitate the use of all HSL packages in Julia.
    JuliaHSL is based on the Meson build system, unlike the other HSL packages, and eases cross-compilation with BinaryBuilder.jl.
    This distinctive feature allows to provide an HSL_jll.jl package, a pre-built version of JuliaHSL to be readily used in the Julia ecosystem.
    We describe its use through HSL.jl and Ipopt.jl.

  • 11h45 - 12h10

    Optimization solvers in JuliaSmoothOptimizers

    • Tangi Migot, prés., Polytechnique Montréal

    In this presentation, we give an overview of the recent progress regarding the continuous nonlinear nonconvex optimization solvers implemented in the JuliaSmoothOptimizers (JSO) organization. We introduce the new package JSOSuite.jl, a unique interface between users and JSO solvers.