26th Simon Stevin Lecture on Optimization in Engineering

"Algorithmic Optimization: new challenges in the old field"

Yurii Nesterov
Department of Mathematical Engineering, Université catholique de Louvain (UCL)

Center for Operations Research and Econometrics (CORE)

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Abstract

During the last decades, Optimization Theory was one of the most developing fields of Computational Mathematics. Now it consists of several powerful approaches, which can treat problems of very big size up to a high accuracy. In many cases, an intelligent use of problem structure allows to overcome the efficiency bounds of the standard optimization theory. At the same time, new randomized algorithms open a possibility of solving problems of practically unlimited dimension. Theoretical complexity analysis of optimization methods became a powerful tool for designing the new schemes, which are able to prove their superiority both in theory and in practical computations. Awareness of all these developments is important for people interested in different applications of optimization technique.

In this lecture, we describe the state of art in Convex Optimization. We start from discussion of general principles of complexity analysis and explain the key elements of classification of optimization problems and efficiency of optimization schemes.

Biographical Information

Yurii Nesterov is professor at the Department of Mathematical Engineering at the Catholic University of Louvain (UCL).

He studied at the Moscow State University where he obtained his master degree in 1977. He obtained his PhD degree in Applied Mathematics at the Institute of Control Sciences, Moscow, in 1984. Until 1992 he was researcher at the Central Economical and Mathematical Institute of USSR Academy of Sciences. In 1993 he became a professor at the Center for Operations Research and Econometrics (CORE) at INMA, Université Catholique de Louvain, where he is until today. Yurii Nesterov made important contributions to many areas of optimization, in particular Black-Box Convex Optimization, the theory of self-concordant functions and Interior-Point Methods, General Nonlinear Optimization, Positive polynomials and sums of squares, and approximate solutions of combinatorial problems. Among his many honors, he received the "George B. Dantzig prize" in 2000, which is awarded triennially by SIAM and the Mathematical Optimization Society for research which by its originality, breadth and scope has a major impact on the field of mathematical optimization and he also got the "John von Neumann Theory Price" from INFORMS in 2009.

About the Lecture Series:

The "Simon Stevin Lecture Series on Optimization in Engineering" is set up in order to promote optimization in engineering. For this aim, every quarter of the year an outstanding international scholar is invited to report on latest progress in the development of optimization algorithms and their applications in engineering.

Simon Stevin (1548-1620) was a Flemish mathematician and engineer. Among other, he helped to advance the use of decimal fractions, was the first to explain the tides by the attraction of the moon, and discovered the hydrostatic paradox. He made numerous inventions, among them a wind propelled carriage with sails, the "land yacht", which once impressed Prince Maurice of Orange as it moved faster than horses, in around 1600 on the beach between Scheveningen and Petten. Simon Stevin was fond of promoting the use of science in daily life and in craftmanship, and translated various mathematical terms into dutch. Among other, he introduced the dutch word for mathematics, "wiskunde".