Design and analysis of bilevel optimisation algorithms

Bilevel optimisation models are used in quantitative decision-making models when we are required to take into account multiple objective functions. The goal is to choose a vector that minimizes an upper level objective function, where our choice is constrained to be from the set of vectors which minimize a lower level objective function. This problem enjoys a rich theoretical structure, and also finds applications in various fields including transportation, revenue management, energy markets, logistics, and machine learning. This project aims to develop new algorithms for a class of convex bilevel optimisation models, through appropriate adaptation of algorithms traditionally used to solve single-level problems (such as gradient descent and Frank-Wolfe). We aim to design algorithms that enjoy convergence guarantees for both upper- and lower-level functions, which has not been achieved in prior literature. We will supplement our theoretical results with a numerical study to demonstrate the efficacy of our methods.

Tran Khanh Hung Giang

University of Sydney

Tran Khanh Hung Giang is currently a third-year student majoring in Mathematics and Business Analytics at University of Sydney. His research interest is finite dimensional mathematical programming, particularly continuous optimization. He is currently working on developing algorithms for convex bilevel optimization. Other than that, he is also interested in optimal control theory and statistical machine learning. Over the years, he has earned a gold medal in Vietnamese Mathematical Olympiad Contest for Undergraduate Students and other scholarships awarded by the departments corresponding to his majors at University of Sydney.

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