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Seminar
Department of Systems Engineering and Engineering Management
The Chinese
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Title |
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From Incomplete Data to Decision Making: Structured
Convex Optimization Approaches |
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Speaker |
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Dr. Shiqian MA |
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Institute for Mathematics and its Applications (IMA) |
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Date |
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May 3, 2012 (Thursday) |
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Time |
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11:15 a.m. - 12:30 p.m. |
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Venue |
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Room 513 |
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William M.W. Mong Engineering
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(Engineering Building Complex Phase 2) |
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CUHK |
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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.
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Biography:
Shiqian Ma is currently
an NSF postdoctoral associate in the Institute for Mathematics and Its
Applications (IMA) at |
************************* ALL ARE WELCOME ************************
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Host |
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Prof. Duan Li |
Tel |
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(852)
3943-8316/8323 |
Email |
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Enquiries |
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Prof. Nan Chen or Prof. Sean X. Zhou |
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Department of Systems Engineering and Engineering
Management |
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CUHK |
Website |
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