Modern convex optimization: Duality, Algorithms, Solutions and Interpretations – prof Tamas Terlaky

A PhD course offered to the Information Engineering PhD program in June 2019 (see the calendar)

Optimization methodology is the engine of prescriptive analytics. This short course gives a gentle, rigorous introduction to modern convex optimization models and algorithms. Duality provides optimality conditions and serve as the platform of algorithm design. First we focus on duality in linear optimization (LO) and convex conic linear optimization (CLO) problems. CLO includes the LO, second order conic and semidefinite optimization problems, which are solvable by Interior Point Methods (IPMs) in polynomial time, and also the NP-hard classes of copositive and completely positive CLO problems. Robust LO models will motivate the introduction of second order conic optimization problems. Then algorithmic concepts, such as pivot algorithms and interior point methods (IPMs) are discussed. Initialization of the algorithms, the computational cost and efficient computation of an iterative step, and characteristics of the produced optimal solutions are discussed. As time allows we shortly available software packages, sensitivity analysis, and some applications will be discussed. Note: Preliminary knowledge of optimization, operations research models and methods is a plus, but everyone with good linear algebra and multi-dimensional calculus skills should be able to follow the course.

Tamas Terlaky: Biographical Sketch 

 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 was a Canada Research Chair in Optimization, and 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, Fellow of INFORMS, and Vice President 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. He is class of 2018 Fellow of SIAM. His research interest includes high performance optimization algorithms, optimization modeling and its applications. ****************************************************************************************