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Research Profile

Professor Jeyakumar is an applied mathematician and internationally recognised leader in mathematical optimization, renowned for advancing the theory, methodology, and computational tools that drive innovation across diverse areas of science and engineering. ÌýBy integrating rigorous mathematical analysis with innovative computational methods, he develops solutions that are not only theoretically sound but also robust and implementable in practice.

A hallmark of his research is the ability to transform intricate mathematical concepts into actionable optimisation frameworks that address uncertainty, enhance decision-making, and improve system performance. His pioneering contributions span nonlinear optimisation and robust optimisation, and machine learning–inspired mathematical models, shaping how challenging optimisationÌý problems are formulated and solved.

Driven by both intellectual curiosity and practical impact, Professor Jeyakumar combines deep theoretical insight with a focus on applicability. His work has shaped new paradigms for managing uncertainty and broadening the scope of optimisation technology.

Through leading publications, high-profile international collaborations, and the mentorship of emerging researchers, Professor Jeyakumar continues to influence the mathematical optimisation community worldwide.

Education

PhD in Optimisation, University of Melbourne.

AWARDS & ACHIEVEMENTS

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PRIZESÌý

• 2025:ÌýMarguerite Frank AwardÌýfor the Best Paper ofÌýEURO Journal on Computational Optimization in 2024

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

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

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RECENT GRANTS

• 2025-2027, ARC Discovery Project Grant ($471,300)(with G. Li and M. Dressler): Quantifying Uncertainty of Risk-Aware Optimization for Safe Decision-Making

• 2025-2027, ARC Discovery Project Grant ($483,000)(with G. Li): Taming Hard Optimization in Measure Spaces for Modern Applications

• 2024, ºÚÁÏÍø´óÊÂ¼Ç 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,ÌýºÚÁÏÍø´óÊÂ¼Ç 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, ºÚÁÏÍø´óÊÂ¼Ç 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

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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

Optimization is the mathematics used for finding the best possible (i.e., optimal) decision from a range of available alternatives based on clearly defined objectives and constraints. Optimization technology provides mathematical principles and methods, numerical algorithms, and software for making complex technical and management decisions across various disciplines. This makes optimization a vital part of many advancements in science, commerce, and engineering, and a key technology of modern inventions such as machine learning and artificial intelligence

Major Research Goals

To advance optimization as a transformative technology for innovation, enabling smarter decision-making in an uncertain world.

Specific Objectives

To develop and apply principles of optimization to bring rigorous approaches to improve management and technical decisions

To provide an advanced mathematical framework to solve practical optimization problems in science, engineering, commerce, and medicine.

Research in Detail

Real-world optimization often deals with problems of decision-making under uncertainty, arising from incomplete information, unknown parameters, or forecasting errors. His current research is focused on developing advanced optimisation approaches that not only account for uncertain parameters but also lead to implementable solutions.

One area of current research develops mathematical approaches and methodologies for uncertainty quantification, which is a task that quantifies the effects of random events by taking into account the likelihoods of different realizations of input parameters and embeds this information into the optimization process.

Recent research in collaboration with a postgraduate student developed an advanced distributionally robust optimization framework and computational methods for studying classes of uncertainty quantification and risk minimization problems, including machine learning models.

One research article that grew out of this work received Marguerite Frank AwardÌýfor the Best Paper ofÌýEURO Journal on Computational Optimization in 2024Ìý

Further collaborative work with postgraduate and postdoctoral researchers successfully applied these techniques to Alzheimer’s disease detection via handwriting analysis, and portfolio management and stock selection.

A second area of research focuses on analysis, methods, and applications of convex optimization over measure spaces. We examine a variety of topics, such as the convex optimization models arising from best approximation, machine learning problems of large-scale data classification and feature selection.

A third strand of research examines deterministic 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.

Many of the recent 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 recent project examined 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.Ìý

Some of his past 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

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Nowadays, optimization and sophisticated computer models are widely used to improve performance in many industrial problems and emerging scientific applications. It is an interesting and challenging area of mathematical research. My current research project contains exciting components that are suitable for honours projects and Ph.D. programs. On-going Ph.D. Project (2023-2025): Robust Optimization under Risk and Data UncertaintÌý

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.

New projects starting this year examine distributionally robust optimization approaches to machine learning models of feature selection in the face of data uncertainty and dynamic decision-making problems. 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) <

He is interested in talented prospective postgraduate students/postdocs/honours students with interests in these areas.

TEACHING & OUTREACH

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