1. Speaker: Prof. Samir Adly, Université de Limoges, France

https://www.unilim.fr/pages_perso/samir.adly/

Title: Quasistatic evolution variational inequalities and sweeping process

Abstract:
In this talk, we study a new variant of the Moreau’s sweeping process with velocity constraint. Based on an adapted version of the Moreau’s catching-up algorithm, we show the well-posedness (in the sense existence and uniqueness) of this problem in a general framework. We show the equivalence between this implicit sweeping process and a quasistatic evolution variational inequality.
It is well-known that the variational formulation of many mechanical problems with unilateral contact and friction lead to an evolution variational inequality. As an application, we reformulate the quasistatic antiplane frictional contact
problem for linear elastic materials with short memory as an implicit sweeping process with velocity constraint. The link between the implicit sweeping process and the quasistatic evolution variational inequality is possible thanks to some standard
tools from convex analysis and is new in the literature.

2. Speaker: Prof. Yury Nesterov,CORE/INMA, Université Catholique de Louvain, Belgium

https://uclouvain.be/fr/repertoires/yurii.nesterov

Title: Relative Smoothness: New Paradigm in Convex Optimization

Abstract:
Development and computational abilities of optimization methods crucially depend on the auxiliary tools provided to them by the method’s designers. During the first decades of Convex Optimization, the methods were based either on the proximal setup, allowing Euclidean projections onto the basic feasible sets, or on the linear minimization framework, which assumes a possibility to minimize a linear function over the feasible set. However, recently it was realized thatany possibility of simple minimization of an auxiliary convex function leads to the efficient minimization methods for some family of more general convex functions, which are compatible with the first one. This compatibility condition, called relative smoothness, was firstly exploited for smooth convex functions (Bauschke, Bolt and Teboulle, 2016) and smooth strongly convex functions (Lu, Freund and Nesterov, 2018). In this talk we make the final step and show how to extend this framework onto the class of nonsmooth functions. We also discuss possible consequences and applications.

3. Speaker: Prof. Nikolai Osmolovskii, Systems Research Institute,
Polish Academy of Sciences, Poland

https://www.researchgate.net/profile/Nikolai_Osmolovskii

Title: Necessary conditions for an extended weak minimum in optimal control problems with Volterra-type integral equations on a variable time interval

Abstract:
We discuss an optimal control problem with Volterra-type integral
equations, considered on a non-fixed time interval, subject to
endpoint constraints of equality and inequality type, mixed
state-control constraints of inequality and equality type, and pure
state constraints of inequality type. The main assumption is the
uniform linear-positive independence of the gradients of active
mixed constraints with respect to the control. We formulate
first-order necessary optimality conditions for an extended weak
minimum, the notion of which is a natural generalization of the
notion of weak minimum with account of variations of the time. The
conditions obtained generalize the corresponding ones for problems
with ordinary differential equations.

This is a joint work with Andrei V. Dmitruk.

4. Speaker: Prof. Janez Povh, University of Ljubljana, Slovenia

https://www.fs.uni-lj.si/en/faculty_of_mechanical_engineering/staff/alphabetically/2016090108013607/

Title: High-performance optimization

Abstract:
High-Performance Computing (HPC) is –with its state-of-the-art computing and storage infrastructure and with the related knowledge– an ecosystem that is essential for scientific research and industrial development. European Commission (EC) often points out the opportunities and challenges at the interface of Big Data, High-Performance Computing and Mathematics. Recent HiPEAC Vision 2017 clearly states that Mathematics and Algorithms for extreme scale HPC systems is one out of seven current EU research priorities related to HPC. Nevertheless, the recent results of Partnership for advanced computing (PRACE) reveal that mathematical research community, including mathematical optimization, rarely decides to use these tools, although they usually do research in hard mathematical optimization problems.

In the first part of the talk we will review the possibilities that the strongest supercomputers in EU offer to mathematical optimization community: what is current best public HPC infrastructure, how to get access to it, how to get necessary skills.

In the second part of the paper we will present a parallel Branch and Bound (B&B) based algorithm to solve to optimality small to medium size instances of non-convex quadratic binary problems with linear constraints. It is is available as on-line solver BiqBin running on the supercomputer owned by University of Ljubljana, Faculty of mechanical engineering. This algorithm encompasses best non-linear optimization techniques and is carefully encoded to run efficiently in parallel using state-of-the-art libraries for parallel linear algebra operations. It’s on-line availability demonstrates new ways how to bring high-performance scientific code closer to scientific users. We will present few implementation details and numerical results obtained by this code.