2025/01/01 by Nathan Allaire, Sébastien Le Digabel, Allaire, Nathan +3
Computer Science · Mathematics · #Stochastic Gradient Optimization Techniques #Numerical methods in inverse problems #Optimization and Variational Analysis
paper · pdf · doi:10.13140/rg.2.2.32728.97288
We introduce iR2N, a modified proximal quasi-Newton method for minimizing the sum of a smooth function f and a lower semi-continuous prox-bounded function h, allowing inexact evaluations of f, its gradient, and the associated proximal operators. Both f and h may be nonconvex. iR2N is particularly suited to settings where proximal operators are computed via iterative procedures that can be stopped early, or where the accuracy of f and ∇ f can be controlled, leading to significant computational savings. At each iteration, the method approximately minimizes the sum of a quadratic model of f, a model of h, and an adaptive quadratic regularization term ensuring global convergence. Under standard accuracy assumptions, we prove global convergence in the sense that a first-order stationarity measure converges to zero, with worst-case evaluation complexity O(ε-2). Numerical experiments with ℓp norms, ℓp total variation, and the indicator of the nonconvex pseudo p-norm ball illustrate the effectiveness and flexibility of the approach, and show how controlled inexactness can substantially reduce computational effort.