Joint seminar of Department of Numerical Analysis and Scientific Computing and International Centre of Research and Postgraduate Training in Mathematics, Institute of Mathematics, Vietnam Academy of Science and Technology.
Speakers: Prof. Felipe Lara (University of Tarapacá, Chile) and Dr. Vu Thi Huong (IM, VAST and ZIB, Germany).
Location: Room 301, building A5, Institute of Mathematics (18 Hoang Quoc Viet, Nghia Do, Ha Noi).
Date: Tuesday morning, August 18th, 2026.
Schedule:
09h00-09h45: On Debreu-Koopmans Theorem for Additively Decomposed Quasiconvex Functions and Its Applications (talk given by Prof. Felipe Lara)
09h45-10h00: Coffee break
10h00-11h00: Double-AI in Bibliometric Analysis: Large Language Models meet Optimization at scale (talk given by Dr. Vu Thi Huong).
Information of the first talk: Speaker: Prof. Felipe Lara
Title: On Debreu-Koopmans Theorem for Additively Decomposed Quasiconvex Functions and Its Applications
Abstract: The Debreu-Koopmans theorem [1] shows that if a separable function $h(x_1, \ldots, x_n) = \sum^n_{i=1} h_i (x_i)$ is quasiconvex, then at most one $h_i$ might be nonconvex and, as a consequence, when all components $h_i$ are quasiconvex, $h$ is not quasiconvex and it is not known to which class of functions $h$ belongs, giving rise to the Debreu-Koopmans problem. In this talk, we introduce the class of (strongly) star quasiconvex functions [4] and we prove that $h$ is (strongly) star quasiconvex if and only if all components $h_i$ are (strongly) star quasiconvex [2] and, as a consequence, we solves the Debreu-Koopmans problem. This result has strong implications in economic theory, since formally bridges classical diversification theory with behavioral economics, as it implies that separable $S$-shaped value (Sigmoid) functions from Prospect Theory [3] are star quasiconvex. Finally, and if the time allows us, we present potential applications in economics and block-coordinate optimization.
[1] G. Debreu, T.C. Koopmans. Additively decomposed quasiconvex functions. Math. Programm. 24:1-38, 1982.
[2] F. Lara. On Debreu-Koopmans theorem for additively decomposed quasiconvex functions. arXiv: 2603.17088, 2026.
[3] D. Kahneman, A. Tversky. Prospect theory: an analysis of decision under risk. Econometrica. 47(2):263-292, 1979.
[4] P.Q. Khanh, F. Lara. Star quasiconvexity: a unified approach for linear convergence of first-order methods beyond convexity. arXiv: 2510.24981, 2025.
Information of the second talk:
Speaker: Dr. Vu Thi Huong
Title: Double-AI in Bibliometric Analysis: Large Language Models meet Optimization at scale
Abstract: Academic performance indicators and university rankings rely heavily on bibliometric analysis. Recent advances in large language models (LLMs) provide powerful semantic representations of scientific publications, while large-scale citation databases such as Web of Science and OpenAlex enable the analysis of scholarly networks at unprecedented scale. Extracting reliable and interpretable knowledge from these data, however, requires principled mathematical models and scalable algorithms. In this talk, I will first present our vision of Double-AI, combining Artificial Intelligence with Algorithmic Intelligence, for bibliometric analysis at scale. Then, focusing on community detection in citation networks, I will discuss how optimization and variational analysis enable scalable algorithms, sparse and interpretable community memberships, and stable clustering solutions under network perturbations. The presentation is illustrated using real-world citation networks with up to billions of citation links. The talk is based on recent and ongoing research of the project Fully Algorithmic Librarian (https://fan.zib.de/).
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