Radu Ioan Boţ

Radu I. Boț is a Romanian mathematician and an academic. He is a Professor as well as the Dean of the Faculty of Mathematics and Head of the Institute of Mathematics at the University of Vienna.

Boț's research focuces on convex analysis, convex optimization, nonsmooth optimization, and monotone operators. His works have been published in academic journals such as SIAM Journal on Optimization, Mathematical Programming, Foundations of Computational Mathematics, Journal of Differential Equations and Journal of the European Mathematical Society.

Education Boț completed his Diploma and Master of Science degrees in Mathematics from Babeș-Bolyai University, Cluj-Napoca, in 1998 and 1999, respectively. He subsequently completed his Ph.D. at Chemnitz University of Technology in 2003. In 2008, he obtained his Habilitation (Dr. rer. nat. habil.), and the following year he was granted the title of Privatdozent (PD) by the same university. Subsequently, he extended Farkas’ Lemma to systems with finite and infinite convex constraints, using two duality frameworks: extended Fenchel and Fenchel–Lagrange duals, and showed strong duality results that unified and generalized classical convex optimization theory. Together with Wanka, he introduced a weaker conjugate epigraph-based regularity condition that ensured Fenchel duality in infinite-dimensional optimization and was applied to the strong conical hull intersection property of convex sets. In 2009, he co-authored the book titled Duality in Vector Optimization, wherein he focused on duality theory in vector optimization, filling a literature gap by providing a comprehensive research-oriented treatment intended for researchers and graduate students in mathematics and optimization. In the subsequent year, he authored the book Conjugate Duality in Convex Optimization. The book explored advanced convex optimization, focusing on conjugate duality, regularity conditions, biconjugate calculus, and Fenchel duality, while developing new duality frameworks and applying them to monotone operators for researchers and graduate students. He also proposed primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone operators, which rely on an inexact Douglas-Rachford method, and investigated their convergence properties.

In collaboration with Csetnek and Hendrich, Boț developed and analyzed an inertial Douglas–Rachford splitting algorithm for monotone inclusions, proved convergence, extended it to structured operators, and demonstrated applications to primal–dual convex optimization with numerical experiments in clustering and location theory. In collaboration with Nguyen, he introduced an inertial continuous-time model with an asymptotically vanishing term for minimizing continuously differentiable convex functions under linear equality constraints, proving fast convergence of the primal-dual gap, feasibility measure, and objective value, together with weak convergence of the trajectory to a primal-dual optimal solution. He also addressed minimax optimization in machine learning, proving novel global convergence guarantees for stochastic alternating gradient descent ascent in challenging non-convex–non-concave settings, relevant to training GANs and adversarial models. More recently, he introduced a Fast Optimistic Gradient Descent Ascent (OGDA) method, in both continuous and discrete time, establishing convergence of the generated trajectories and iterates while achieving the best-known convergence rates among schemes for solving monotone equations.