KAUST Research Workshop on Optimization and Big Data
Prof. Terlaky is Chair of the Department of Industrial and Systems Engineering and George N. and Soteria Kledaras ’87 Endowed Chair Professor at Lehigh U.Prior to his appointment at Lehigh U., where he served as the Chair of ISE 2008-2017, Prof. Terlaky has taught at Eötvös U., Budapest, Hungary; Delft University of Technology, Delft, Netherlands; McMaster U., ON, Canada. At McMaster he also served as the founding Director of the School of Computational Engineering and Science.Prof. Terlaky has published four books, edited over ten books and journal special issues and published over 180 research papers. Topics include theoretical and algorithmic foundations of mathematical optimization (e.g., invention of the criss-cross method, oriented matroid programming), design and analysis of large classes of interior point methods, computational optimization, worst case examples of the central path, nuclear reactor core reloading optimization, oil refinery and VLSI design and robust radiation therapy treatment optimization, and inmate assignment optimization.Prof. Terlaky is Founding Honorary Editor-in-Chief of the journal, Optimization and Engineering. He has served as associate editor of ten journals and has served as conference chair, conference organizer, and distinguished invited speaker at conferences all over the world. He was general Chair of the INFORMS 2015 Annual Meeting, a former Chair of INFORMS' Optimization Society, Chair of the ICCOPT Steering Committee of the Mathematical Optimization Society, currently Chair of the SIAM Activity Group on Optimization, he is Fellow of the Fields Institute, and Fellow of INFORMS. He received the MITACS Mentorship Award for his distinguished graduate student supervisory record, and the Award of Merit of the Canadian Operations Research Society. November 2017 he received the Wagner Prize of INFORMS and the Egerváry Award of the Hungarian Operations Research Society.His research interest includes high performance optimization algorithms, optimization modeling and its applications.
The basic concepts of Interior Point Methods (IPMs) were introduced by Frish in 1950’s, and further developed in the 1960’s, among others by Fiacco-McCormick (SUMT) and Dikin (Affince scaling). By the early 70’s it was concluded that, mostly due to numerical instability, IPMs most probably will not be viable algorithms for solving large scale optimization problems.
Karmarkar’s 1984 paper and the subsequent “Interior Point Revolution” fundamentally changed the landscape of optimization. IPMs become the method of choice to solve large-scale linear optimization problems, new classes of conic and convex optimization problems become efficiently solvable. The new powerful algorithmic and software tools opened new areas of applications. In this talk we walk through the history of IPMs, highlight the scientific and computer technology advances that make the Interior Point revolution possible.
The perceptron and von Neumann algorithms are known to be closely related, like duals. A deterministic rescaled version of the perceptron algorithm was proved to be polynomial by Pena and Soheil. Recently, Chubanov proposed a method which solves homogeneous linear equality systems with positive variables in polynomial time. Chubanov's method can be considered as a column-wise rescaling procedure. We adapt Chubanov's method to the von Neumann problem, and so we design a polynomial time column-wise rescaling von Neumann algorithm. This algorithm is the first variant of the von Neumann algorithm with polynomial complexity.
Joint work with Dan Li and Kees Roos