7th IMA Conference on Numerical Linear Algebra and Optimization

Event


Date: -

Please Note: Fully Accessible Conference, Daily Delegate Rate Available, Accommodation Options Available

University of Birmingham

Birmingham, B15 2TT, UK

Wednesday June 29, 2022
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Friday July 1, 2022
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Europe/London 7th IMA Conference on Numerical Linear Algebra and Optimization University of Birmingham, , Birmingham, B15 2TT, UK PROGRAMME ABSTRACT BOOK The IMA is pleased to announce the Seventh Biennial IMA Conference on Numerical Linear Algebra and Optimization. […] Fully Accessible Conference, Daily Delegate Rate Available, Accommodation Options Available Event Link: https://ima.org.uk/12530/7th-ima-conference-on-numerical-linear-algebra-and-optimization/

7th IMA Conference on Numerical Linear Algebra and Optimization


PROGRAMME

ABSTRACT BOOK

The IMA is pleased to announce the Seventh Biennial IMA Conference on Numerical Linear Algebra and Optimization.

The success of modern codes for large-scale optimization is heavily dependent on the use of effective tools of numerical linear algebra. On the other hand, many problems in numerical linear algebra lead to linear, nonlinear or semidefinite optimization problems. The purpose of the conference is to bring together researchers from both communities and to find and communicate points and topics of common interest. This Conference has been organised in cooperation with the Society for Industrial and Applied Mathematics (SIAM).

Conference topics include any subject that could be of interest to both communities, such as:

• Direct and iterative methods for large sparse linear systems.
• Eigenvalue computation and optimization.
• Large-scale nonlinear and semidefinite programming.
• Effect of round-off errors, stopping criteria, embedded iterative procedures.
• Optimization issues for matrix polynomials
• Fast matrix computations.
• Compressed/sparse sensing
• PDE-constrained optimization
• Distributed computing and optimization
• Applications and real time optimization

 

Invited Speakers

Gabriele Eichfelder (TU Ilmenau)
Pierre Antoine Absil (University of Louvain)
Zlatko Drmac (University of Zagreb)
Moritz Diehl (University of Freiburg)
David Silvester (University of Manchester)
Frank Curtis (Lehigh University)

 

Multiobjective Optimization without Scalarization: Heterogeneous Problems with Expensive Functions, Gabriele Eichfelder

In multiobjective optimization, one considers optimization problems with several competing objective functions. For instance, in engineering, a design often has to be stable and light at the same time. A classical approach to such optimization problems is to formulate suitable parameter-dependent single-objective replacement problems, called scalarization, such as considering a weighted sum of the objective functions. Then, the parameters are varied and the scalarized problems are solved iteratively.

However, many multiobjective optimization problems have a structure where a scalarization is not a suitable approach for an efficient procedure. In this talk, we give an introduction to the basic concepts and classical approaches in multiobjective optimization. Then, we present such classes of multiobjective optimization problems where it is better not to scalarize. For specific heterogeneous problems, where one of the objective functions is assumed to be an expensive black-box function while the other objectives are analytically given, we give more details on a numerical approach. That method uses the basic trust region concept by restricting the computations in every iteration to a local area. The objective functions are replaced by suitable models which reflect the heterogeneity of the objective functions.

IFISS: A computational laboratory for investigating incompressible flow problems, David Silvester

The Incompressible Flow & Iterative Solver Software (IFISS) package contains software that can be run with MATLAB or Octave to create a computational laboratory for the interactive numerical study of incompressible flow problems. It includes algorithms for discretisation by mixed finite element methods and a posteriori error estimation of the computed solutions, together with state-of-the-art preconditioned iterative solvers for the resulting discrete linear equation systems. In this talk we give a flavour of the main features and illustrate its applicability using several case studies. We will demonstrate that the software is a valuable tool in the present era of open science and reproducible research.

Optimization on manifolds: methods and applications, Pierre-Antoine Absil

This talk concerns applications of differential geometry in numerical optimization. They arise when the optimization problem can be formulated as finding an optimum of a real-valued cost function defined on a smooth nonlinear search space. Oftentimes, the search space is a “matrix manifold”, in the sense that its points admit natural representations in the form of matrices. In most cases, the matrix manifold structure is due either to the presence of certain nonlinear constraints (such as orthogonality or rank constraints), or to invariance properties in the cost function that need to be factored out in order to obtain a nondegenerate optimization problem. Manifolds that come up in practical applications include the rotation group SO(3) (generation of rigid body motions from sample points), the set of fixed-rank matrices (low-rank models, e.g., in collaborative filtering), the set of 3×3 symmetric positive-definite matrices (interpolation of diffusion tensors), and the shape manifold (morphing).

In the recent years, the practical importance of optimization problems on manifolds has stimulated the development of geometric optimization algorithms that exploit the differential structure of the manifold search space. In this talk, we give an overview of geometric optimization algorithms and their applications, with an emphasis on the underlying geometric concepts and on the numerical efficiency of the algorithm implementations.

Robust and reliable numerical linear algebra‐applications and implementations, Zlatko Drmač

The goal of this talk is twofold.
First, we show how to deploy the state of the art numerical linear algebra perturbation theory and algorithms to curbill‐conditioning that precludes successful numerical implementation of sophisticated methods in applications.  Some instances of ill conditioning(loss of accuracy due to large matrix condition numbers) do not reflect the intrinsic sensitivity of the problem, but are due to a particular algorithm executed infinit precision arithmetic.  Suitably constructed algorithms can compute with particularly structured backward errors that render such ill‐conditioning harmless and deliver more accurate results with a more favorable measure of sensitivity.  For instance, we can compute the (generalized) eigen values of positive definite matrices (pencils) to the best possible accuracy‐as accurately as the data deserves‐independent of the traditional condition number.
As case studies we use selected problems from the computational analysis of nonlinear systems (Koopman operator based spectral analysis and data driven identification/learning of nonlinear dynamical systems).
In particular, we show how to compute with notoriously ill‐conditioned Vandermonde and Cauchy matrices, and how to solve linear least squares problems with the matrix that involves the Khatri Rao product of a triangular and a Vandermonde matrix.  Further, we discuss computing matrix approximation of the infinitezimal generator of the Koopman operator semigroup.  This involves matrix logarithm of potentially severely ill‐conditioned matrices.  We show how implicit preconditioning helps alleviate the problem.
Secondly, we discuss the issue of the reliability of the numerical software.  We use a case study example (rank revealing QR factorization) to show how a  numerical instability and a pure software bug can remain undetected for decades in the state of the art libraries such as LAPACK, ScaLAPACK, Matlab, despite many tests (all passed)and extensive usage.  We conclude with a general discussion on the importance of numerical analysis of computational algorithms, that must include the concrete software implementation.

Numerical Optimal Control for Differential Equations with State Dependent Switches and Jumps, Moritz Diehl

Optimal control problems for dynamical systems with state dependent switches are inherently non-smooth and non-convex and therefore difficult to treat numerically. They appear in many fields including switched power electronic converters, that can be controlled by advanced technologies like model predictive control (MPC) if one is able to solve nonsmooth optimal control problems in a few microseconds. This became possible due to recent algorithmic progress including the development of a library of Basic Linear Algebra Subroutines for Embedded Optimization (BLASFEO).  Systems with state dependent jumps – e.g. a bouncing billiard ball – are even more difficult to treat than systems with switches, as they lead to discontinuous state trajectories. We present two recently developed ideas: First, the method of Finite Elements with Switch Detection (FESD) to numerically solve optimal control problems of switched systems with high order of accuracy.  Second, the time-freezing idea for optimal control problems with state jumps, which allows one to reformulate these problems into the easier class of problems with switches, which can then be treated by the FESD method. Both methods are illustrated with numerical examples including the challenging optimal control problem of a hopping robot with ground contact and friction that should detect an optimal jump sequence to a final position in the presence of holes. Joint work with Armin Nurkanovic, Sebastian Albrecht, Bernard Brogliato, Jonas Hall, Florian Messerer, Gianluca Frison and Benjamin Stickan.

Registration

Registration is currently open at  https://my.ima.org.uk/

If you are an IMA Member or you have previously registered for an IMA conference, then you are already on our database. Please “request a new password” using the email address previously used, to log in.
Registration Closes – 23 June 2022

If you are attending the conference please use the hashtag #IMALinearAlgebra2022 and tag the IMA on socials!

Early Bird Conference Fees

IMA/SIAM Member – £395.00
Non IMA/SIAM Member – £450.00
IMA/SIAM Student – £215.00
Non IMA/SIAM Student – £225.00

Conference Fees will increase by £20 on 22 May 2022

*Conference fees include refreshments and lunches throughout the conference.

Day Delegate rate:
A Day Delegate rate is also available for this Conference if you would like to attend one of the scheduled Conference days. If you would like to find out more information about our Day Delegate rate, please contact us at conferences@ima.org.uk

Accommodation

The IMA have booked accommodation at Edgbaston Park Hotel on hold for delegates on a first-come, first-serve basis. The room is £90 Single occupancy, B&B which will be available to book until 16/05/2022.

If you are interested in booking at this rate, please contact the Conferences Department for the booking code.

Organising Committee

Michal Kocvara, University of Birmingham (co-chair) (SIAM representative)
Daniel Loghin, University of Birmingham (co-chair)
Coralia Cartis, University of Oxford
Nick Gould, Rutherford Appleton Laboratory
Philip Knight, University of Strathclyde
Jennifer Scott, Rutherford Appleton Laboratory
Valeria Simoncini, University of Bologna

COVID 
We plan to run conferences in person as advertised; however, if government guidance changes then we will consider holding affected events online using Zoom.

Contact information

For general conference queries please contact the Conferences Department, Institute of Mathematics and its Applications, Catherine Richards House, 16 Nelson Street, Southend-on-Sea, Essex, SS1 1EF, UK.

E-mail: conferences@ima.org.uk              Tel: +44 (0) 1702 354 020

This Conference has been organised in cooperation with the Society for Industrial and Applied Mathematics (SIAM) 
Published