|Professor of Chemical Engineering at the Imperial College, London
Title: Deterministic global optimisation of mixed integer nonlinear bilevel programs
Abstract: Bilevel optimization problems are relevant to numerous applications, including economics, planning and a range of engineering problems (parameter estimation, flexibility analysis). We present a deterministic global optimisation algorithm, the Branch-and-Sandwich algorithm, for bilevel problems with nonlinear outer and inner problems. This branch-and-bound approach is based on the formulation of bounding problems for the inner and outer problems, together with a branching/tree management strategy that allows branching on the inner variables. We present an extension of the algorithm to mixed-integer problems and introduce BASBL, our implementation within the open-source MINOTAUR framework. We also introduce BASBLib, an extensive online library of bilevel benchmark problems collected from the literature including problems derived from practical applications and designed to enable contributions from the bilevel optimization community. We use the problems from BASBLib to analyze the performance of BASBL using different algorithmic options, including different bounding schemes, branching, and node selection strategies.
(credits to Remigijus Paulavičius and Polyxeni-Margarita Kleniati)
|Professor of Optimization at the University of Edinburgh
Title: Interior Point Methods and Beyond
Abstract: In this talk I will discuss an impact made by interior point methods (IPMs) for optimization. IPMs deliver efficient and reliable solution techniques for linear, quadratic, nonlinear, second-order cone and semidefinite programming problems and excel when dimensions of problems are large. They also provide an inspiration for a design of more general schemes for solving other classes of optimization problems by using an inexact Newton method embedded into a continuation scheme.
|Silver Professor of Computer Science at Courant Institute of Mathematical Sciences, New York University
Title: Teaching Numerical Optimization: How to Move from Theory to Code?
Abstract: Those who teach numerical optimization almost always start with theory. But it is also important for students to learn about computational and software issues that arise in writing code for solving real-world problems. This talk will discuss a variety of ideas for achieving this often-overlooked transition.