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Variational Analysis and Optimisation Seminar

Variational Analysis and Optimisation Seminar

Start Date

September 23, 2020

End Date

September 23, 2020

Registration

Closed

Time: September 23rd, 2020 at 05:00 PM AEST

Variational Analysis and Optimisation Seminar
Dear colleagues,
The next talk in the Variational Analysis and Optimisation Webinar series will be given by Regina Burachik on September 23rd, 2020, 05:00 PM AEST. Here are the details:
(17:00 AEST = 15:00 in China = 14:00 in Vietnam = 10:00 in Israel = 9:00 in most of Europe.)
Join Zoom Meeting:https://uwa.zoom.us/j/98686167020?pwd=RXUveWhVVVRNWUFUazJrZUdOS2pQZz09
Password: 437959
Meeting ID: 986 8616 7020
Speaker: Regina Burachik (UniSA)
Talk: A Primal–Dual Penalty Method via Rounded Weighted-L1 Lagrangian Duality
Abstract: We propose a new duality scheme based on a sequence of smooth minorants of the weighted-ℓ1 penalty function, interpreted as a parametrized sequence of augmented Lagrangians, to solve nonconvex constrained optimization problems. For the induced sequence of dual problems, we establish strong asymptotic duality properties. Namely, we show that (i) the sequence of dual problems is convex and (ii) the dual values monotonically increase to the optimal primal value. We use these properties to devise a subgradient based primal–dual method, and show that the generated primal sequence accumulates at a solution of the original problem. We illustrate the performance of the new method with three different types of test problems: A polynomial nonconvex problem, large-scale instances of the celebrated kissing number problem, and the Markov–Dubins problem. Our numerical experiments demonstrate that, when compared with the traditional implementation of a well-known smooth solver, our new method (using the same well-known solver in its subproblem) can find better quality solutions, i.e., “deeper” local minima, or solutions closer to the global minimum. Moreover, our method seems to be more time efficient, especially when the problem has a large number of constraints.
This is a joint work with C. Y. Kaya (UniSA) and C. J. Price (University of Canterbury, Christchurch, New Zealand)
Please forward this information to anyone you think could be interested in this seminar series.
Best regards,
Hoa Bui (Curtin), Minh Dao (Federation Uni), Alex Kruger (Federation Uni), Guoyin Li (UNSW), Vera Roshchina (UNSW), Matthew Tam (UniMelb)