An Augmented Lagrangian Method For Nonconvex Optimization Problems with Conically-Convex Constraints

Dr. William Kong

Abstract: This talk presents and analyzes a novel nonlinear inner accelerated inexact proximal augmented Lagrangian (NL-IAIPAL) method for solving smooth nonconvex composite optimization problems with nonlinear 𝒦-convex constraints, i.e., the constraints are convex with respect to the order given by a closed convex cone 𝒦. Each NL-IAIPAL iteration consists of inexactly solving a proximal augmented Lagrangian subproblem by an accelerated composite gradient (ACG) method followed by a full Lagrange multiplier update. Under some mild assumptions, it is shown that NL-IAIPAL generates an approximate stationary solution of the constrained problem in O(log(1/𝜌)/𝜌³) ACG iterations, where 𝜌 > 0 is a given tolerance. Numerical experiments are given to illustrate the computational efficiency of the presented method.

Speaker’s Bio: William Kong is a Postdoctoral Research Associate in the Multiscale Methods group at Oak Ridge National Laboratory. His mathematical background is primarily in continuous optimization and, more specifically, developing and analyzing large-scale nonconvex optimization algorithms. He holds a B.Math. in Mathematical Finance from the University of Waterloo together with an M.Sc. in Computational Science & Engineering, and a Ph.D. in Operations Research from the Georgia Institute of Technology. Currently, he is researching and implementing new sparse grid methods for applications in high dimensional quadrature and interpolation.

Last Updated: October 8, 2021 - 10:47 am