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Seminar: Largest Small n-Polygons: Numerical Results and Conjectured Optima

July 22, 2019 @ 2:00 pm - 3:00 pm

Title: Largest Small n-Polygons: Numerical Results and Conjectured Optima

Speaker: János D. Pintér

Affiliation: Department of Industrial and Systems Engineering, Lehigh University

Location: 218 Huxley Building

Time: 14:00 – 15:00


Abstract. LSP(n), the largest small polygon with n vertices, is defined as the polygon of unit diameter that
has maximal area A(n). Finding the configuration LSP(n) and the corresponding A(n) for even
values n >= 6 is a long-standing challenge that can be also perceived as class of hard global
optimization problems. We present numerical solution estimates for all even values 6 <= n <= 80,
using the AMPL model development environment with the LGO global-local solver engine option.
Our results are in close agreement with the results obtained by other researchers who tackled the
problem using exact approaches (for 6 <= n <= 20), and with the best results obtained using general
purpose numerical optimization software (for selected values from the range 6 <= n <= 100). Based
on our numerical results, we also present a regression model based estimate of {A(n)} for all even
values n >= 6.


Bio. János D. Pintér is a researcher and practitioner with over four decades of experience. His
general professional interests are related to Computational Optimization, Data Analytics, and
Operations Research (O.R.). His more specific primary area of expertise is nonlinear optimization,
including model, algorithm and software development, with a range of applications.
He received his M.Sc. in the area of Applied Mathematics / Operations Research from
Eötvös Loránd University, Hungary; Ph.D. in Probability Theory / Stochastic Optimization from
Moscow State University; and D.Sc. in Mathematics / Global Optimization from the Hungarian
Academy of Sciences.

As of 2019, Dr. Pintér wrote and edited ten books. He is also the author/co-author of more
than 200 journal articles, book chapters, proceedings contributions, book reviews, and research
reports. His monograph titled Global Optimization in Action received the 2000 INFORMS
Computing Society Prize for Research Excellence.

Among other professional affiliations, he serves on the editorial board of the Journal of
Global Optimization, and he is an editor of the book series SpringerBriefs in Optimization. He also
served as Global Optimization vice-chair of the INFORMS Optimization Society, and as a member
(later chair) of the Managing Board of EUROPT. Currently, he is a member of the Canadian and
the Hungarian Operations Research Societies, INFORMS, and EUROPT.
He has worked and presented lectures in about 40 countries of the Americas, Europe, the
Middle East, and the Pacific Region. His LGO software – with links to modeling languages and
scientific-technical computing systems – has been in use at hundreds of academic, business,
government, and research organizations.

In 2016, Dr. Pintér joined the Department of Industrial and Systems Engineering at Lehigh
University as a Professor of Practice. Since that time, he has been teaching a range of O.R. related
courses for undergraduate and graduate students, as well as ISE in-class and online (distance)
courses for healthcare engineering professionals.



July 22, 2019
2:00 pm - 3:00 pm