École Nationale Supérieure de
Techniques Avancées

Abstract

We develop method R2N, a modified quasi-Newton method for minimizing the sum of a smooth 𝑓 with Lipschitz gradient and lower semi-continuous prox-bounded h. Both 𝑓 and h may be nonconvex and may be bound constrained. At each iteration, our method computes a step by minimizing the sum of a convex quadratic quasi-Newton model of 𝑓 , a model of h, and an adaptive quadratic regularization term. A step may be computed by way of methods R2 [2] or TRDH [21]. In variant R2N-DH, the model of 𝑓 is diagonal, which allows us to compute a step without resort to a subproblem solver for a few separable h that are relevant in applications. R2N-DH can also be used as subproblem solver inside R2N. We establish global convergence of a first-order stationarity measure to zero and a worst-case evaluation complexity bound of 𝑂(𝜖−2) to bring said measure below 𝜖 ∈ (0, 1). Furthermore, we extend our analysis to consider worst-case complexity in more general scenarios, even when the approximation of the Hessian is unbounded. We describe our Julia implementation and report numerical experience on inverse problems, and a minimum-rank matrix completion problem.

Available Versions of this Item

• A Proximal Modified Quasi-Newton Method for Nonsmooth Regularized Optimization (deposited 28 nov. 2024 15:19) [Currently Displayed]
  • A Proximal Modified Quasi-Newton Method for Nonsmooth Regularized Optimization (deposited 19 janv. 2024 09:34)