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A Matrix-Free Trust-Region Newton Algorithm for Convex-Constrained Optimization

Drew P. Kouri(dpkouri***at***sandia.gov)

Abstract: We describe a matrix-free trust-region algorithm for solving convex-constrained optimization problems that uses the spectral projected gradient method to compute trial steps. To project onto the intersection of the feasible set and the trust region, we reformulate and solve the dual projection problem as a one-dimensional root finding problem. We demonstrate our algorithm's performance on multiple problems from data science and PDE-constrained optimization. Our algorithm shows superior performance when compared with five existing trust-region and spectral projected gradient methods, and has the added benefit that it is simple to implement.

Keywords: Nonconvex Optimization, Convex Constraints, Trust Regions, Spectral Projected Gradient, Large-Scale Optimization, Newton’s Method

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Nonlinear Optimization

Category 3: Infinite Dimensional Optimization

Citation: Submitted for publication, Sandia National Laboratories, 2020.

Download: [PDF]

Entry Submitted: 01/26/2021
Entry Accepted: 01/26/2021
Entry Last Modified: 01/26/2021

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