Operational Research and Applied Statistics

Link for registration

https://docs.google.com/forms/d/1ra3TSRYtuXxZFPOYhLLyfezzCw6tIWoPHRwnRtjJ-fM

Detailed Program

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Day 1: August 4th, 2022

Day 2: August 5th 2022

Speakers and Abstracts

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Operational Research and Game Theory – An Introduction and Applications

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The first part of the talk will provide a general introduction to OR and some of its real-world applications. I will discuss about the stages that OR can help solve an industrial problem; that is, from communicating to decision makers to problem formulation and solution approaches. The second part will go through the technical aspects of a specific application on how banks can make optimal decisions on their ATM network investment and can fairly share the cost of the network in the UK. A new game theory model with results on the Nash equilibrium existence and techniques for fast computation of large-scale numerical problems are presented.

Relaxed-inertial proximal point algorithms for problems involving strongly quasiconvex functions

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Introduced in in the 1970’s by Martinet for minimizing convex functions and extended shortly afterwards by Rockafellar towards monotone inclusion problems, the proximal point algorithm turned out to be a viable computational method for solving various classes of optimization problems, in particular with nonconvex objective functions.
We propose first a relaxed-inertial proximal point type algorithm for solving optimization problems consisting in minimizing strongly quasi-convex functions whose variables lie in finitely dimensional linear subspaces. The method is then extended to equilibrium problems where the involved bifunction is strongly quasi-convex in the second variable.

Possible modifications of the hypotheses that would allow the algorithms to solve similar problems involving quasi-convex functions are discussed, too. Numerical experiments confirming the theoretical results, in particular that the relaxed-inertial algorithms outperform their “pure” proximal point counterparts [3, 4], are provided, too.

This talk is based on joint work [1, 2] with Felipe Lara and Raúl Tintaya Marcavillaca (Universidad de Tarapacá).

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