Seminar


       Department of Systems Engineering and Engineering Management,

                    The Chinese University of Hong Kong

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Title:
A quantile-based robust linear programming

Speaker:
Dr. L. Jeff Hong
Department of Industrial Engineering and Logistics Management
The Hong Kong University of Science and Technology

Date : November 2, 2005 (Wednesday)

Time : 5:30 p.m. - 6:30 p.m.

Venue : Room 513, William M.W. Mong Engineering Building

(Engineering Building Complex Phase 2), CUHK



Abstract:
Linear programming (LP) is one of the most widely used operations-research
tools. LP problems can typically be solved very accurately and efficiently.
However, parameters of a LP are often estimated from data that come from
random distributions. Ignoring the estimation errors may result in suboptimal
solutions or infeasible solutions. In this talk we propose a robust
formulation of the LP problem. It optimizes a quantile of the objective
function while ensures that each constraint is satisfied with a high and
predetermined probability. We propose a Monte-Carlo (MC) optimization method
to solve the problem and show that the method converges with probability 1 and
converges in an exponential rate. We suggest to solve the MC problem using a
gradient-based approach, and we further develop a direct gradient-estimation
scheme that does not require resimulation. We also extend our method to solve
portfolio management problems with value-at-risk constraints. Numerical
results show that our method is accurate and efficient.

This is a joint work with Xiangtong Qi of HKUST.

　

Bio:
L. Jeff Hong is an assistant professor in the Department of Industrial
Engineering and Logistics Management at The Hong Kong University of Science
and Technology. He received his Ph.D. in the Department of Industrial
Engineering and Management Sciences at Northwestern University. His research
interests include design and analysis of simulation models and optimization
via simulation.