On 1 March 2026, at VNUHCM–University of Science (HCMUS), researcher Mai Văn Duy successfully defended a doctoral dissertation in Applied Mathematics. The thesis, entitled “Optimality conditions and duality for some classes of adjustable robust optimisation problems”, was conducted under the academic supervision of Associate Professor Nguyễn Minh Tùng and Associate Professor Nguyễn Lê Hoàng Anh.

The research focuses on optimality conditions and duality models for several classes of adjustable robust optimisation problems. These include adjustable robust linear, convex, non-smooth, and multi-objective convex optimisation. Central to this study is the construction of non-adjustable equivalent forms for adjustable robust optimisation problems involving general data.

By establishing these equivalent forms, the adjustable robust optimisation problem is transformed into a standard robust optimisation model—a framework extensively studied within optimisation theory, supported by a wealth of analytical tools and algorithms. This approach simplifies the structure of the original problem and facilitates the application of established techniques within the field of robust optimisation.

The equivalent models were developed within a comprehensive framework sufficiently broad to encompass most classes of adjustable robust optimisation problems, including linear, convex, and non-smooth cases. Notably, the proposed methodology does not require restrictive assumptions regarding the structure of the uncertainty set, thereby extending the applicability of these models to complex real-world scenarios.

Building upon this foundation, the thesis employs tools from robust optimisation and variational analysis to systematically investigate regularity conditions and constraint qualifications. The work establishes optimality conditions for various types of solutions in adjustable robust multi-objective problems and analyses the corresponding duality models. These findings offer novel contributions that supplement and advance previous research on adjustable robust optimisation, strengthening the theoretical framework and providing a basis for future algorithmic developments.

Beyond the theoretical significance, the results provide a foundation for analysing computational complexity and developing efficient solution methods for optimisation problems under uncertainty.

Throughout the doctoral candidacy, researcher Mai Văn Duy published four international scientific papers related to the dissertation within the ISI/Scopus database. These publications comprise two Q1, one Q2, and one Q3 ranked journals, with a cumulative Impact Factor of 5.7.

The Examination Committee concluded that the dissertation fully satisfies the requirements for a doctorate in Applied Mathematics. The research holds significant scientific value and serves as a formal reference for advanced study and specialised research within the field.