Colloquium/Seminar

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Event(s) on May 2012


  • Friday, 4th May, 2012

    Title: Fractional Calculus with Applications
    Speaker: Prof. Changpin Li, Department of Mathematics, Shanghai University, China
    Time/Place: 14:30  -  15:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: It has been found that fractional calculus play a crucial role in modeling anomalous diffusion, time-dependent materials and processes with long-range dependence, allometric scaling laws, as well as power law in complex systems. In this talk, we firstly introduce some fundamental definitions of fractional derives and fractional integral. Then we compare the fractional ordinary differential equations with the classical differential equations. The real and potential applications of fractional calculus, as well as our works in this regard, are also presented. In the last part, possible challenging problems in the field of fractional calculus are listed to stimulate potential research interests.


  • Monday, 7th May, 2012

    Title: From Incomplete Data to Decision Making: Structured Convex Optimization Approaches
    Speaker: Dr. Shiqian Ma, Institute for Mathematics and Its Applications, University of Minnesota, USA
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Decision making from incomplete data is a very important topic in Operations Research. Incomplete data occur frequently in different areas in practice. For example, in stock return data from financial markets, incomplete data occur because there are hidden factors that cannot be observed in the market. Another example is the rating data from online recommendation systems, in which the data are sometimes manipulated by some people in purpose. In this talk, we show that a lot of decision making problems with incomplete data arising from Finance, Statistics and Machine Learning can be formulated as structured convex optimization problems. In particular, we consider the formulations that require the solutions to have sparse or low-rank properties. These problems are usually large-scale with millions of variables and constraints and thus are very challenging to solve. We propose several alternating direction methods that take advantage of the special structures of the problems to solve them. Specifically, we propose alternating linearization methods (ALM) for solving convex optimization problems with two sets of variables. We show that our basic and accelerated ALMs need respectively O(1/eps) and O(1/sqrt(eps)) iterations to obtain an eps-optimal solution. To the best of our knowledge, these are the first iteration complexity results that have been given for alternating direction type methods. We then propose alternating proximal gradient method (APGM) that can solve convex optimization problems with three or more sets of variables. We prove that APGM globally converges to an optimal solution under very mild assumptions. Numerical results on problems arising from Finance, Statistics, Machine Learning, Facility Location and Compressed Sensing are shown to demonstrate the efficacy of the proposed approaches.


  • Wednesday, 23rd May, 2012

    Title: Estimation and Selection in Additive and Generalized Linear Models
    Speaker: Ms. Zhenghui FENG, Department of Mathematics, Hong Kong Baptist University, Hong Kong
    Time/Place: 15:00  -  16:00
    FSC1216, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: This thesis consists of two main topics: selection and estimation in additive models and generalized linear models. In the topic of additive models, two kinds of additive models, the multi-index additive models and the nonparametric additive models are studied. Selection and estimation in generalized linear models and transformation models are studied in the topic of generalized linear models.