¶¶Òõ¶ÌÊÓƵ

ABOUT ME

Ìý

Biography

I am an applied mathematician. My research interests are in mathematical optimization. It is an area of mathematics that directly deals with the problem of making the best possible choice from a set of feasible choices. It seeks to understand how we achieve the best possible choice and how we can use this knowledge to improve management and technical decisions in science, engineering, and commerce. Thinking in terms of choices is common in our cognitive culture and searching for the best possible choice is a basic human desire. Thus models of optimization arise every day as management and technical decisions in many areas of human activity. I develop mathematical principles and methods for identifying and locating solutions for a wide range of optimization models.

Education

PhD in Optimization, University of Melbourne

AWARDS & ACHIEVEMENTS

Ìý

PRIZESÌý

• 2019: Joint winner of the 2019 Journal of Global Optimization Best Paper Prize,

• 2017: Winner of the 2015 Optimization Letters Best Paper Prize,Ìý

Ìý

MY RECENT GRANTS

• 2024, UNSW Science Goldstar Award ($30,000) (with G. Li and Ho-Nguyen):ÌýNew Optimisation with Uncertainty Quantification for Best Decision-Making.
• 2021-2023, ARC Discovery Project Grant ($400,000) (with G. Li):ÌýData-Driven Multistage Robust Optimization - The New Frontier in Optimization
• 2018-2020, ARC Discovery Project Grant ($401,706) (with G. Li) : New mathematics for multi-extremal optimization and diffusion tensor imaging
• 2017,ÌýUNSW Science Gold Star AwardÌý($40,000), (withÌýG. Li, and T. D. Chuong): Numerically Certifiable Mathematics for Multi-Extremal Global Optimization.Ìý
• 2012-2014, ARC Discovery Project GrantÌý($330,000) (with G. Li): New theory and methods of robust global optimization
• 2011, UNSW Goldstar AwardÌý ($30,000)ÌýÌýInnovative approaches to solving optimization problems affected by data uncertainty optimizationÌý
• 2010-2013, ARC Discovery Project Grant($285,543): A new improved solution to global optimization over multi-variate polynomials
• 2007-2009, ARC Discovery Project Grant ($246,000): Quadratic support function technique to solving hard global nonconvex optimization problems
• 2006-2008, ARC Linkage International Award ($22,250):Continuous optimization with linear matrix inequality systems
• 2005-2007, ARC Discovery Project Grant ($403,000) (with T. Hoang and B. Vo) : Convex optimization for control, signal processing and communications
• 2004-2006, ARC Discovery Project Grant ($283,752) (with A.M. Rubinov): Necessary and Sufficient Conditions in Global Continuous Optimization

Ìý

MOST CITED ARTICLES

• 2012, The paper ``V. Jeyakumar and G. Li. Exact SDP relaxations for classes of nonlinear semidefinite programming problems, Operation Research Letters, 40 (2012), no. 6, 529–536.'' published in Operation Research Letters (ERA: A), was listed asÌýthe most cited 25 articlesÌýfrom 2012-2016.
• 2011,ÌýThe paper ``V. Jeyakumar, G. Li and G. M. Lee, A robust von Neumann minimax theorem for zero-sum games under bounded payoff uncertainty, Volume 39, Issue 2, March 2011, 109-114.'' published in Operation Research Letters (ERA: A), was listed as theÌýmost cited 25 articlesÌýfrom 2011-2015.

RESEARCH

Ìý

My Research Goals

• To understand and improve Mathematics of Decision Making
• To develop and characterize mathematical principles of optimization
• To apply the principles of optimization to bring rigorous approaches to improve management and technical decisions
• To provide advanced mathematical framework to solve practical optimization problems in science, engineering, commerce and medicine

Ìý

My Research in Detail

I am interested in a range of topics in Optimization. One strand of my research examines optimization models in the face of data uncertainty. We examine mathematical approaches to finding robust best solutions for uncertain optimization models that are immunized against data uncertainty. We develop mathematical principles and methods for identifying and locating such solutions of a wide range of optimization models.

One paper, grown out of our recent work in this area, won the Optimization Letters Journal Best Paper Award for 2015.

A current project examines multi-objective optimization models in the presence of conflicting objectives and data uncertainty. It is a joint work with Dr Guoyin Li (Associate Professor), who is a member of the Optimization group at UNSW.

A second area of my research focuses on analysis, methods, and applications of duality theory and associated techniques of convex optimization. We have examined a variety of topics such as the convex optimization models arising from the machine learning problems of large-scale data classification.

Some of my recent research projects in this area have involved technologically significant problems such as the development of screening algorithms for HIV-associated neurological disorders, produced by a new optimization procedure. This was a result of successful research collaboration between the research group in Optimization within Mathematics and the HIV Epidemiology and Clinical Research Group at St Vincent's Hospital. The research outcome on screening algorithms was published in the British Journal, of HIV Medicine.

What did HIV clinicians read on Medscape in 2011?
When HIV specialists come to Medscape HIV/AIDS what are they most interested in reading? ... Starting with number 10, here is our most-read content for 2011 in HIV. 10. Lifelong Antiretroviral Therapy Unsustainable, Experts Say. 9. Can We Stop Monitoring CD4 counts Entirely in HIV? ... 2. Curing HIV? And the number-one most-read article by HIV clinicians on Medscape in 2011 was...

A Screening Algorithm for HIV-Associated Neurocognitive Disorders, Cysique, Murray, Dunbar, Jeyakumar, Brew, HIV Medicine, 11:642-649, 2011.Ìý

Much of my studies in this area are fundamental, but these mathematical studies have a flow-through effect for addressing major challenges of modern problems such as the development of clinically based decision support tools in medical science. A current project is examining two-stage convex optimization with applications to medical decision-making optimization models of radiation therapy planning. Another ongoing collaborative project examines applications of robust optimization for characterizing Huntington's disease onset.

One study examines emerging applications of algebraic geometry to optimization over polynomials. A good understanding of convex sets in algebraic geometry will lead to insights into solving complex optimization problems involving polynomials.

Another project investigates bi-level optimization models. These models arise when two independent decision-makers, ordered within a hierarchical structure, have conflicting objectives. Optimization models of this kind appear in resource allocation and planning problems.

A new project starting this year examines optimization approaches to multi-stage optimization problems in the face of evolving uncertainty. The dynamic decision-making problems under uncertainty are multi-stage robust optimization problems, where uncertainties evolve (in stages), rendering traditional optimization solutions sub-optimal.Ìý This issue is particularly prevalent in medical decision-making, where a patient's condition can change during the treatment. The project aims to develop optimization principles to identify true optimal solutions to these multi-stage problems and develop associated methods to find those solutions.

Recently completed honours thesis topics include:

(i) Feature Selection under Data Uncertainty via DC Programming (2022)

(ii) Supervised Machine Learning under Data Uncertainty (2020)

(iii) Two-stage Adjustable Robust Optimization (2019)

(iv) Bilevel optimization and Principal-Agent Problems (2017)

(v) Portfolio Optimization under Data Uncertainty (2010)

(vi) Optimization approaches to simultaneous classification and feature selection (2007)

(vii) Semidefinite programming approaches to support vector machines (2003)

(viii) Optimization methods in data mining (2000) <

I am interested in talented prospective postgraduate students/postdocs/honours students with interests in these areas.

TEACHING & OUTREACH

Ìý

Courses I teachÌý

Professional affiliations and service positions

• >Associate Editor, The Journal of Optimization Theory and Applications
• Associate Editor, Journal of Global Optimization
• Associate Editor, Minimax Theory and Its Applications