Date: 28 September 2018
Morning Session: 9:10am-11:30am (Tea Break 10.10am-10.30am)
Afternoon Session: 1:30pm-4:00pm (Tea Break 2.40pm-3pm)
Title: Progressive Hedging Algorithms in Stochastic Optimization
First Day Objective of the Workshop
One of the central challenges in operations research and business analytics is to find a good approach to dealing with multi-stage stochastic optimization problems. The concept of a stochastic variational inequality has recently been articulated in a new way that is able to cover, in particular, the optimality conditions for multistage stochastic programming problems. This allows the progressive hedging algorithm, one of the long-standing methods for solving such optimization problems under convexity, to be used to solve multistage stochastic variational inequality problems under monotonicity. A code has been developed for stochastic linear variational inequality in a two-stage formulation.
A pre-workshop assignment will be distributed to the participants, which include a description of a stochastic two-stage optimization problem with data. The participants are encouraged to build an optimization model of their own and bring it to the workshop.
The first day of the workshop starts with a morning lecture on an introduction to stochastic optimization, stochastic variational inequality and the progressive hedging algorithm, which include a possible two-stage stochastic optimization model for the pre-workshop assignment problem. In the afternoon, a MATLAB template will be demonstrated for solving general two stage linear stochastic variational inequality problems. In particular, we will demonstrate how to input data and to run the program code to solve the pre-workshop assignment problem. At the end of the afternoon session, the interested participants can stay and try to use the program code of the progressive hedging algorithm on their own laptops (if they have MATLAB installed in their laptops, the MATLAB code will be placed in a dropbox for free download).
This workshop targets at PHD students and researchers in management and engineering, who have been working on various decision models under uncertainty and may need an effective way to solve convex stochastic optimization problems. A MATLAB programming capability is a plus. We encourage the participants to bring their own laptops with MATLAB.
Shapiro, A, Dentcheva D, and Ruszczyski A. Lectures on Stochastic Programming: Modelling and Theory. SIAM, Philadelphia, 2009.
Rockafellar R. T. and Sun J. “Solving monotone stochastic variational inequalities and complementarity problems by progressive hedging”, to appear in Mathematical Programming.No. 242 on http://sites.math.washington.edu/~rtr/papers.html
Speakers: Prof Jie SUN, and Prof Min Zhang
Prof Jie Sun
Prof Jie Sun (PhD in Applied mathematics, University of Washington, 1986)’s area of expertise includes continuous optimization and decision under uncertainty. Specifically, he has been a frontier researcher in semismooth Newton’s methods, interior point methods, and stochastic variational inequalities. He was a winner of Outstanding Researcher Award of National University of Singapore and was one of the highly cited mathematicians 2002-2012 selected by Thomson Reuters. Currently he is a Distinguished Research Professor at Curtin University, Australia and Part-time Professor at National University of Singapore.
Dr Min Zhang
Dr Min Zhang received the PhD degree in Applied Mathematics from Tianjin University, China, in 2016. She was awarded a scholarship of the China Scholarship Council to study as a joint PhD student at Curtin University in 2015. Currently she is a research associate at Curtin University, working with Prof. Jie Sun on the topics of stochastic variational inequalities and progressive hedging algorithm.