Prof. Goran Lesaja and Prof. Yurii Nesterov will hold a workshop on the elements of IPMs for linear and convex optimization
WORKSHOP
Introduction to Interior-Point Methods
Professor Goran Lesaja,
Senior Research Fellow, Corvinus University, Budapest
Emeritus Professor, Georgia Southern University, USA
Professor Yurii Nesterov
Research Professor, Corvinus University, Budapest
Emeritus Professor, Center for Operations Research and Econometrics, UCLouvain, Belgium
Interior-point methods (IPMs) have become a standard component of modern optimization software packages, yet many graduate students encounter these powerful algorithms only indirectly—through solvers—without a clear understanding of the underlying theory. This two-hour workshop aims to bridge that gap by introducing the basic elements of IPMs for linear optimization and generalizations to convex (conic) optimization in an accessible and self-contained manner.
The first part of the workshop will cover fundamental concepts such as the central path, neighborhoods of the central path, the role of Newton’s method in determining the search directions, and convergence and polynomial complexity of IPMs for linear optimization.
The second part of the workshop will cover generalizations of IPMs to convex (conic) optimization problems via fundamental concepts of self-concordant barriers.
In the third part of the workshop, optimization software package MOSEK will be used to illustrate the performance of IPMs on several examples from linear and conic optimization, giving participants concrete insight into how IPMs work in practice. The hard copy of the “MOSEK modeling-cookbook” will be available for the participants of the workshop.
No prior knowledge of IPMs is assumed; a solid background in linear algebra and basic calculus is sufficient. The workshop is intended primarily for researchers, as well as students, who wish to gain a basic understanding of one of the most widely used algorithmic frameworks in modern optimization.
Goran Lesaja is Emeritus Professor in the Department of Mathematical Sciences at Georgia Southern University (GSU) and a Senior Research Fellow at the Corvinus Center for Operations Research, Corvinus Institute for Advanced Studies, Corvinus University, Budapest, Hungary. He received his B.S. and M.S. degrees in Mathematics from the University of Zagreb, Croatia, and his Ph.D. in Applied Mathematical and Computational Sciences from the University of Iowa in 1996.
Professor Lesaja has held faculty positions at Georgia Southern University since 1996, where he was promoted to full Professor in 2011 and was appointed Emeritus Professor in August 2025. Throughout his career he has held several distinguished visiting appointments, including the Davis 68 Distinguished Chair and Visiting Professor at the United States Naval Academy in Annapolis, Maryland (2020–2021), Visiting Associate Professor at the Georgia Institute of Technology (2003–2004), Visiting Professor at Yaşar University in Izmir, Turkey (2013–2014), and sabbatical positions at the Technical University of Delft, Netherlands, and the University of Maryland Baltimore County.
His research specializes in optimization theory and applications, with a particular focus on interior-point methods (IPMs) for Linear Complementarity Problems (LCPs), kernel-function-based algorithms, and optimization over symmetric cones. He has made fundamental contributions to the unified analysis of kernel-based IPMs for P*(κ)-LCPs and to the development of full Newton-step feasible and infeasible algorithms for LCPs and weighted LCPs. He has also worked on applications of optimization models and IPMs in statistical disclosure limitation. His work has appeared in leading optimization journals including the SIAM Journal on Optimization, the Journal of Optimization Theory and Applications, and Optimization Methods and Software. He has been supported by external funding from the NSF, the Hungarian National Research, Development and Innovation Office (NKFIH), the National Natural Science Fund of China, and the Netherlands Scientific Organization, among others. He is an active member of the international optimization community, serving on editorial boards and as an editor or guest editor to several prestigious optimization journals and organizing special sessions, as well as delivering plenary talks at major conferences.
Professor Lesaja has supervised several M.S. students and a Ph.D. student and served as a member on many M.S. and Ph.D. thesis defense committees. For over two decades he organized and prepared students at GSU for the Putnam Mathematical Competition and the Mathematical Contest in Modeling. For his work, Dr. Lesaja has received several institutional honors including the GSU Award for Excellence in Instruction (2009) and the GSU Award for Excellence in Service (2011).
Yurii Nesterov earned his Master’s in 1997 from Moscow State University, and his Ph.D. in Applied Mathematics in 1984 from the Institute of Control Sciences. He held researcher positions at the Central Economic Mathematical Institute (1977–1992) before joining UCLouvain and its Center for Operations Research and Econometrics (CORE), Belgium, in 1993, where he is now Emeritus Professor. During his long teaching and research career at UCLouvain, he was an advisor
to numerous M.S. and Ph.D. students. Since February 2024, he has joined Corvinus University of Budapest in Hungary as a Research Professor. He also holds visiting research positions at several universities in China.
Yurii Nesterov is internationally recognized for his fundamental contributions to optimization theory and methods, including the development of accelerated gradient methods (Nesterov’s momentum), optimal methods for smooth convex minimization, smoothing and cubic regularization methods for optimizing non-smooth functions, and the theory of self-concordant functions and barriers. Together with Arkadi Nemirovski, he developed the theoretical foundations of interior-point methods for convex programming, establishing polynomial-time
complexity results that revolutionized the field. Their monograph, Interior-Point Polynomial Algorithms in Convex Programming, and his Introductory Lectures on Convex Optimization remain cornerstone references. His work has had a transformative impact across optimization, machine learning, and computational mathematics.
His outstanding contributions have been recognized by prestigious international awards: Dantzig Prize (2000), the John von Neumann Theory Prize (2009), the EURO Gold Medal (2016), and the WLA Prize (2023).
