VA & Opt Webinar: Christopher Price (University of Canterbury)

Title: A direct search method for constrained optimization via the rounded ℓ₁ penalty function.

Speaker: Christopher Price (University of Canterbury)

Date and Time: September 16th, 2020, 17:00 AEST (Register here for remote connection via Zoom)

Abstract: This talk looks at the constrained optimization problem when the objective and constraints are Lipschitz continuous black box functions.   The approach uses a sequence of smoothed and offset ℓ₁ penalty functions. The method generates an approximate minimizer to each penalty function, and then adjusts the offsets and other parameters. The smoothing is steadily reduced, ultimately revealing the ℓ₁ exact penalty function. The method preferentially uses a discrete quasi-Newton step, backed up by a global direction search. Theoretical convergence results are given for the smooth and non-smooth cases subject to relevant conditions. Numerical results are presented on a variety of problems with non-smooth objective or constraint functions. These results show the method is effective in practice.