- A Limited-Memory Quasi-Newton Algorithm for Bound-Constrained Nonsmooth Optimization Nitish Shirish Keskar(keskar.nitishu.northwestern.edu) Andreas Waechter(waechteriems.northwestern.edu) Abstract: We consider the problem of minimizing a continuous function that may be nonsmooth and nonconvex, subject to bound constraints. We propose an algorithm that uses the L-BFGS quasi-Newton approximation of the problem's curvature together with a variant of the weak Wolfe line search. The key ingredient of the method is an active-set selection strategy that defines the subspace in which search directions are computed. To overcome the inherent shortsightedness of the gradient for a nonsmooth function, we propose two strategies. The first relies on an approximation of the $\epsilon$-minimum norm subgradient, and the second uses an iterative corrective loop that augments the active set based on the resulting search directions. We describe a Python implementation of the proposed algorithm and present numerical results on a set of standard test problems to illustrate the efficacy of our approach. Keywords: nonsmooth optimization; bound constraints; quasi-Newton; L-BFGS; active-set method; active-set correction Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Category 2: Nonlinear Optimization (Bound-constrained Optimization ) Citation: Download: [PDF]Entry Submitted: 12/21/2016Entry Accepted: 12/21/2016Entry Last Modified: 12/21/2016Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.