AIME@CZ  2012
Czech workshop on applied mathematics in engineering
7-8 November 2012
Charles Square Campus of the Czech Technical University in Prague, Czech Republic
The Department of Control Engineering & The Center for Machine Perception FEE CTU in Prague


The workshop, organized by Didier Henrion and Tomas Pajdla of the Faculty of Electrical Engineering of the Czech Technical University in Prague, aims at reporting recent achievements in applied mathematics in engineering, and especially at learning what nearby colleagues and close collaborators are doing, with the hope that it may start new collaborations. This is the second workshop of this kind, following a first workshop organized in November 2011.

Date and venue

The workshop takes place on Wednesday 7 and Thursday 8 November 2012, in room G205, building G, on the Charles Square Campus of the Czech Technical University in Prague, Czech Republic. To reach building G, refer to these instructions.


Wednesday 7 November 2012

Thursday 8 November 2012


Vladimír Kučera (bio) Polynomial Equation Approach to Linear Control System Design


Polynomial techniques have made important contributions to systems and control theory. Engineers in industry often find polynomial and frequency domain methods easier to utilize than state equation based techniques. Control theorists show that results obtained in isolation using either approach are in fact closely related.

Polynomial system description provides input-output models for linear systems with rational transfer functions. These models display two important system properties, namely poles and zeros, in a transparent manner. A performance specification in terms of polynomials is natural in many situations; see pole allocation techniques.

A specific control system design technique, called polynomial equation approach, was developed in the 1960s and 1970s. The distinguishing feature of this technique is a reduction of controller synthesis to a solution of linear polynomial equations of specific (Diophantine or Bézout) type.

In most cases, control systems are designed to be stable and to meet additional specifications, such as optimality and robustness. It is therefore natural to design the systems step by step: stabilization first, then the additional specifications each at a time. For this it is obviously necessary to have any and all solutions of the current step available before proceeding any further.

This motivates the need for a parametrization of all controllers that stabilize a given plant. In fact this result has become a key tool for the sequential design paradigm. The additional specifications are met by selecting an appropriate parameter. This is simple, systematic, and transparent. However, the strategy suffers from an excessive grow of the controller order.

This plenary is a guided tour through the polynomial control system design. The origins of the parametrization of stabilizing controllers, called Youla-Kučera parametrization, are explained. Historical and personal notes are added. Standard results on pole placement and H2 control are summarized. New and exciting applications of the parametrization result are then discussed: stabilization subject to input constraints, output overshoot reduction, fixed order controller design, and robust stabilization.

Jan Flusser (bio) The beauty of deconvolution.


This talk is devoted to deconvolution problem in image processing, namely to its ill-posed and ill-conditioned formulation. We present a unified approach to this problem based on a regularized minimization of a proper energy functional. After the explanation of mathematical background, several applications including embedded solution in smartphones will be demonstrated.
Josef Málek (bio) Implicitly constituted fluids and solids: modeling, analysis and computation
Abstract Implicit constitutive theory that is based on the idea of expressing the response of bodies by an implicit relation between the stress and appropriate kinematical variables, is capable of describing some of the material properties that explicit models seem unable to describe. It also provides a less standard interesting structure of the governing equations. After introducing implicit constitutive relations to describe the response of both non-linear fluids and solids, we will present several examples emphasizing the advantages of this framework on three levels: modeling of material responses, theoretical analysis of related boundary values problems and computer simulations.
Fredrik Kahl (bio) Efficient and Robust Optimization Techniques in Computer Vision
Abstrakt There have been major advances in optimization techniques for many problems in computer vision in the last decade. In the first part of this talk, I will focus on graph cuts which is by now a standard tool for applications like image segmentation, stereo and denoising. The method is capable of efficiently computing optimal solutions for large-scale problems with submodular cost functions. It can also be used for approximating hard, non-submodular problems. New results on how to construct the best lower-bounding approximation, the so-called generalized roof dual, will be presented. In particular, a polynomial-time algorithm for computing a solution that attains the bound will be described.

In the second part, another standard tool namely RANSAC will be reviewed. It is one of the most successful approaches for handling the large amounts of outliers occurring in multiple view geometry and registration problems. The general goal of RANSAC is to find the solution which has the maximum number of inliers. However, the method has no guarantee of finding the optimal solution. I will show how one can modify the standard scheme and obtain such guarantees with a polynomial-time algorithm. Other goal functions, such as the truncated L2-norm, will also be considered.
Pavel Trnka Distributed Optimization and Model Predictive Control
Abstract Many large-scale optimization problems arising from practical applications can be effectively decomposed to multiple small problems and solved in coordinated iterations. The talk will introduce decomposition and coordination principles and analogies. Then it will target distribution methods for model predictive control, which is the most successful advanced control strategy used in the industry. Finally a fast coordination method based on a multi-parametric programming will be presented and demonstrated on distributed controller for Barcelona city water distribution network.
Zdeněk Strakoš (bio) Challenges in coupling iterative algebraic computations with modeling and discretisation
Abstract The current state-of-the art of iterative solvers is the outcome of the tremendous algorithmic development over the last few decades and of investigations of {\em how} to solve given problems. In this contribution we focus on Krylov subspace methods and more on the dual question {\em why} things do or might not work in solving practical problems. This requires considering the algebraic computations in the context of the mathematical properties of the underlying model and its discretisation, with the tools ranging from functional analysis to approximation and matrix theory.

We will pose and discuss, in particular, open questions such as what does the spectral information tell us about the behaviour of Krylov subspace methods, to which extent we can relax the accuracy of local operations in {\em inexact} Krylov subspace methods without causing an unwanted delay, how important is considering rounding errors in various algorithmic techniques, whether it is useful to view Krylov subspace methods as {\em matching moment model reduction}, and how the algebraic error can be included into locally efficient and fully computable {a-posteriori} error bounds for adaptive PDE solvers.
Xavier Goaoc (bio) From geometric optimization to nerve theorems ... and back
Abstract  This talk will explore some of the connections between a fundamental problem in computational geometry, the efficient computation of the cylinder best fitting a set of points, and classical questions in discrete geometry, line geometry and topological combinatorics: Helly numbers, geometric permutations, nerve theorems ...
Tomáš Werner (bio) Marginal Equalization in Constraint Networks and Graphical Models over Commutative Semirings
Abstract Constraint propagation, or local consistency, is ubiquitous in constraint satisfaction. Recently, techniques similar to classical constraint propagation have been developed that are applicable to soft versions of constraint satisfaction problems. In computer vision and machine learning, this kind of techiques is known as message passing.

We present a version of constraint propagation that applies to a wide class of generalized constraint satisfaction problems, defined in terms of commutative semirings. This constraint propagation consists in locally transforming the problem to an equivalent problem so that marginals of overlapping problems overlap. The technique is a generalization of the max-sum diffusion algorithm, proposed in 1976 by Schlesinger et al.
Lenka Zdeborová (bio) Compressed sensing: How insight from statistical physics leads to optimality
Abstract Compressed sensing is a revolutionary idea in signal acquisition, allowing to measure signals directly in their compressed form while being able to "decompress" without losses in a tractable way. Algorithms based on linear programming and L1 regularization were the state of the art for this task until recently. Our insight from statistical physics studies leads to an astonishing new compressed sensing scheme: Combining a belief-propagation-like algorithm with a special design of measurements allows to perform not only better than previously, but also to achieve asymptotically the information theoretically best possible performance. My aim is to review these results in a broadly accessible manner letting most of the details for a discussion.

Please, pre-register by sending an e-mail with Subject: "aime@cz 2012" to Eva Matyskova ( to allow us to arrange coffee breaks and lunches for the size of the audience.
Programme and organizing committee: Didier Henrion (henrion at, Tomas Pajdla (pajdla at, Eva Matyskova (matyskov at,
Last updated on 6 October 2012.