Month: May 2020

VA & Opt Webinar: Tien-Son Pham (Uni of Dalat)

Title: Openness, Hölder metric regularity and Hölder continuity properties of semialgebraic set-valued maps

Speaker: Tiến-Sơn Phạm. (Department of Mathematics, University of Dalat, Vietnam)

Date and Time: June 3rd, 2020, 17:00 AEST. (Register here for remote connection via Zoom)

Abstract: Given a semialgebraic set-valued map with closed graph, we show that it is Hölder metrically subregular and that the following conditions are equivalent:
(i) the map is an open map from its domain into its range and the range of is locally closed;
(ii) the map is Hölder metrically regular;
(iii) the inverse map is pseudo-Hölder continuous;
(iv) the inverse map is lower pseudo-Hölder continuous.
An application, via Robinson’s normal map formulation, leads to the following result in the context of semialgebraic variational inequalities: if the solution map (as a map of the parameter vector) is lower semicontinuous then the solution map is finite and pseudo-Holder continuous. In particular, we obtain a negative answer to a question mentioned in the paper of Dontchev and Rockafellar [Characterizations of strong regularity for variational inequalities over polyhedral convex sets. SIAM J. Optim., 4(4):1087–1105, 1996]. As a byproduct, we show that for a (not necessarily semialgebraic) continuous single-valued map, the openness and the non-extremality are equivalent. This fact improves the main result of Pühn [Convexity and openness with linear rate. J. Math. Anal. Appl., 227:382–395, 1998], which requires the convexity of the map in question.  

Seminars

Monash Colloquium: Jon Chapman (Oxford)

Title: Asymptotics beyond all orders: the devil’s invention?

Speaker: Prof. S. Jon. Chapman (Oxford)

Date And Time: 8:30 pm – 10:00 pm AEST, Thu., 14 May 2020.

Venue: Zoom (register here for connection details)

Abstract: The lecture will introduce the concept of an asymptotic series, showing how useful divergent series can be, despite Abel’s reservations. We will then discuss Stokes’ phenomenon, whereby the coefficients in the series appear to change discontinuously. We will show how understanding Stokes phenomenon is the key which allows us to determine the qualitative and quantitative behaviour of the solution in many practical problems. Examples will be drawn from the areas of surface waves on fluids, crystal growth, dislocation dynamics, localised pattern formation, and Hele-Shaw flow.

Seminars

UNSW Seminar: Matthew K. Tam (UniMelb)

Title: Splitting Algorithms for Training GANs

Speaker: Matthew Tam (University of Melbourne)

Date: Thu, 14/05/2020 – 11:05am

Venue: Zoom meeting (connection details here)

Abstract: Generative adversarial networks (GANs) are an approach to fitting generative models over complex structured spaces. Within this framework, the fitting problem is posed as a zero-sum game between two competing neural networks which are trained simultaneously. Mathematically, this problem takes the form of a saddle-point problem; a well-known example of the type of problem where the usual (stochastic) gradient descent-type approaches used for training neural networks fail. In this talk, we rectify this shortcoming by proposing a new method for training GANs that has both: (i) theoretical guarantees of convergence, and (ii) does not increase the algorithm’s per iteration complexity (as compared to gradient descent). The theoretical analysis is performed within the framework of monotone operator splitting.

Seminars