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Dynamical system approaches for solving variational inequalities


   Faculty of Social Sciences

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  Dr Vuong Phan  No more applications being accepted  Funded PhD Project (UK Students Only)

About the Project

Variational inequalities (VIs) are a powerful mathematical model which unifies important concepts in applied mathematics like systems of nonlinear equations, necessary optimality conditions for optimisation problems, complementarity problems, obstacle problems, or network equilibrium problems. Therefore, this model has numerous applications in the fields of mathematical programming, network economics, transportation research, game theory, and regional sciences. Although many progresses in the solution methods for solving VIs have been achieved, most of them are only applicable to VIs governed by monotone operators and, consequently, to convex optimisation. It still requires a lot of work to understand these techniques in the context of non-monotone operators and to apply the obtained results to non-convex optimisation problems. In this project, we will investigate solution methods for solving non-monotone VIs via first and second order dynamical systems. An iterative algorithm can be seen as a discretization of a continuous dynamical system. The study of dynamical systems may shed a new light on the properties of the algorithm, provide Lyapunov functions which are useful in the asymptotic analysis, and often lead to new classes of algorithms.

If you wish to discuss any details of the project informally, please contact Vuong Phan, Operational Research Group, Email: [Email Address Removed]. Tel: +44 (0) 2380 59 4550.

Host Institution

You will be based at the University of Southampton, a research intensive university and a founding member of the Russell Group of elite British universities. In the 2014 Research Excellence Framework, Southampton was ranked 8th for research intensity. In 2017-18, Southampton has been ranked 5th in the UK for research grant income. Besides being recognised as one of the leading research universities in the UK, Southampton has also achieved consistently high scores for its teaching and learning activities. In the Research Excellence framework, 100% of Mathematics research impact and research environment was specifically rated as of internationally excellent or world-leading quality. The broad range of Mathematical Sciences at Southampton gives Southampton a unique ability to contribute to the scientific and social challenges facing society.

Southampton has an excellent track record for optimisation. Statistics and Operational Research groups have existed within Mathematical Sciences since the 1960s. In the early 2000s, the broad multidisciplinary nature of Southampton activity in these areas was recognised through the establishment of the Centre of Operational Research, Management Sciences and Information Systems CORMSIS, which spans Mathematical Sciences and Southampton Business School. Operational Research at the University of Southampton is ranked 34th in the world, and top 10 in the UK, according to the latest QS World Rankings. You will be a member of CORMSIS for the duration of your PhD studies.

Entry Requirements

A very good undergraduate degree (at least a UK 2:1 honours degree, or its international equivalent).

How To Apply

Apply for the research degree programme PhD Mathematical Sciences in the Faculty of Social Sciences.

Applications should be made online.

Applications should include:

Research Proposal

Curriculum Vitae

Two reference letters

Degree Transcripts to date

Apply online: https://www.southampton.ac.uk/courses/how-to-apply/postgraduate-applications.page


Funding Notes

For UK students, Tuition Fees and a stipend of £15,285 tax-free per annum for up to 3.5 years.
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