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The University of Southampton
CORMSIS Centre for Operational Research, Management Sciences and Information Systems

"Utility Preference Robust Optimization", talk by Dr Shaoyan Guo (Dalian University of Technology) Event

Time:
14:00 - 16:00
Date:
8 August 2019
Venue:
54/4011 (L/T 4A), School of Mathematical Sciences, University of Southampton, Highfield Campus, SO17 1BJ

For more information regarding this event, please email Professor Huifu Xu at H.Xu@southampton.ac.uk .

Event details

Utility preference robust optimization (PRO) models are recently proposed to deal with decision making problems where information on decision maker's utility preference is incomplete and has to be elicited through partial information such as questionnaires and pairwise comparisons, and the optimal decision is based on the worst case utility function elicited. In this paper, we examine an extension of the model to situations where the underlying utility functions are nonconcave, the ambiguity set of elicited utility functions is dependent on decision variables and the domain of the utility functions is unbounded. To solve the resulting maximin optimization problem, we propose a piecewise linear approximation (PLA) scheme for the ambiguity set. An immediate benefit of the PLA scheme is that it enables us to solve the inner utility minimization problem by solving a linear programming problem regardless of whether the elicited utility functions are concave or merely increasing or dependent on decision variables. To justify the PLA scheme, we derive an error bound for the approximated ambiguity set and the optimal value of the resulting maximin problem. The error bound provides an interval of the approximated optimal value.

In an effort to address data-driven environment, we derive some stability results which quantify the change of the ambiguity set against variation of problem data and its impact on the optimal value of the PRO model.  Finally, we carry out some numerical results to examine convergence of the optimal values and the worst case utility functions as the number of piecewise linear functions and/or information on the true utility function increases.

Speaker information

Dr Shaoyan Guo, Dalian University of Technology, is a lecturer in the School of Mathematical Sciences, Dalian University of Technology. She obtained a PhD degree in Operational Research from School of Mathematical Sciences, Dalian University of Technology, China in 2016 and then worked as a postdoctoral research fellow in the School of Mathematical Sciences, University of Southampton from 2016 to 2017. Over the past few years, Shaoyan has been actively working on distributionnally robust optimization and preference robust optimization, risk management and matrix conic programming. She has published 7 papers at international journals including SIAM Journal on Optimization and Mathematical Programming.

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