objective-function-free optimization

A Stochastic Objective-Function-Free Adaptive Regularization Method with Optimal Complexity

  • Serge Gratton
  • Sadok Jerad
  • Philippe L. Toint
    • Categories Data Science Algorithms, Nonlinear Optimization Tags , , , ,

    A fully stochastic second-order adaptive-regularization method for unconstrained nonconvex optimization is presented which never computes the objective-function value, but yet achieves the optimal $\mathcal{O}(\epsilon^{-3/2})$ complexity bound for finding first-order critical points. The method is noise-tolerant and the inexactness conditions required for convergence depend on the history of past steps. Applications to cases where derivative evaluation … Read more

    Convergence properties of an Objective-Function-Free Optimization regularization algorithm, including an $\mathcal{O}(\epsilon^{-3/2})$ complexity bound

  • Serge Gratton
  • Sadok Jerad
  • Philippe L. Toint
    • Categories Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , ,

    An adaptive regularization algorithm for unconstrained nonconvex optimization is presented in which the objective function is never evaluated, but only derivatives are used. This algorithm belongs to the class of adaptive regularization methods, for which optimal worst-case complexity results are known for the standard framework where the objective function is evaluated. It is shown in … Read more

    Parametric complexity analysis for a class of first-order Adagrad-like algorithms

  • Serge Gratton
  • Sadok Jerad
  • Philippe L. Toint
    • Categories Stochastic Programming, Unconstrained Optimization Tags , , , , ,

    A class of algorithms for optimization in the presence of noise is presented, that does not require the evaluation of the objective function. This class generalizes the well-known Adagrad method. The complexity of this class is then analyzed as a function of its parameters, and it is shown that some methods of the class enjoy … Read more