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Globalization of SQP-methods in control of the instationary Navier-Stokes equations

Michael Hintermüller, Michael Hinze (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A numerically inexpensive globalization strategy of sequential quadratic programming methods (SQP-methods) for control of the instationary Navier Stokes equations is investigated. Based on the proper functional analytic setting a convergence analysis for the globalized method is given. It is argued that the a priori formidable SQP-step can be decomposed into linear primal and linear adjoint systems, which is amenable for existing CFL-software. A report on a numerical test demonstrates the feasibility...

Globalization of SQP-Methods in Control of the Instationary Navier-Stokes Equations

Michael Hintermüller, Michael Hinze (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A numerically inexpensive globalization strategy of sequential quadratic programming methods (SQP-methods) for control of the instationary Navier Stokes equations is investigated. Based on the proper functional analytic setting a convergence analysis for the globalized method is given. It is argued that the a priori formidable SQP-step can be decomposed into linear primal and linear adjoint systems, which is amenable for existing CFL-software. A report on a numerical test demonstrates the feasibility...

Godunov-like numerical fluxes for conservation laws on networks

Vacek, Lukáš, Kučera, Václav (2023)

Programs and Algorithms of Numerical Mathematics

We describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads. On individual roads, we consider the standard Lighthill-Whitham-Richards model which is discretized using the discontinuous Galerkin method along with suitable limiters. In order to solve traffic flows on networks, we construct suitable numerical fluxes at junctions based on preferences of the drivers. Numerical experiment comparing different approaches is presented.

Goffin's algorithm for zonotopes

Michal Černý (2012)

Kybernetika

The Löwner-John ellipse of a full-dimensional bounded convex set is a circumscribed ellipse with the property that if we shrink it by the factor n (where n is dimension), we obtain an inscribed ellipse. Goffin’s algorithm constructs, in polynomial time, a tight approximation of the Löwner-John ellipse of a polyhedron given by facet description. In this text we adapt the algorithm for zonotopes given by generator descriptions. We show that the adapted version works in time polynomial in the size...

Gradient flow optimization for reducing blocking effects of transform coding

Feng Gao, Xiaokun Li, Xun Wang, William Wee (2004)

International Journal of Applied Mathematics and Computer Science

This paper addresses the problem of reducing blocking effects in transform coding. A novel optimization approach using the gradient flow is proposed. Using some properties of the gradient flow on a manifold, an optimized filter design method for reducing the blocking effects is presented. Based on this method, an image reconstruction algorithm is derived. The algorithm maintains the fidelity of images while reducing the blocking effects. Experimental tests demonstrate that the presented algorithm...

Gradient observability for diffusion systems

El Hassane Zerrik, Hamid Bourray (2003)

International Journal of Applied Mathematics and Computer Science

The aim of this paper is to study regional gradient observability for a diffusion system and the reconstruction of the state gradient without the knowledge of the state. First, we give definitions and characterizations of these new concepts and establish necessary conditions for the sensor structure in order to obtain regional gradient observability. We also explore an approach which allows for a regional gradient reconstruction. The developed method is original and leads to a numerical algorithm...

Graph centers used for stabilization of matrix factorizations

Pavla Kabelíková (2010)

Discussiones Mathematicae Graph Theory

Systems of consistent linear equations with symmetric positive semidefinite matrices arise naturally while solving many scientific and engineering problems. In case of a "floating" static structure, the boundary conditions are not sufficient to prevent its rigid body motions. Traditional solvers based on Cholesky decomposition can be adapted to these systems by recognition of zero rows or columns and also by setting up a well conditioned regular submatrix of the problem that...

Greedy algorithms for optimal computing of matrix chain products involving square dense and triangular matrices

Faouzi Ben Charrada, Sana Ezouaoui, Zaher Mahjoub (2011)

RAIRO - Operations Research - Recherche Opérationnelle

This paper addresses a combinatorial optimization problem (COP), namely a variant of the (standard) matrix chain product (MCP) problem where the matrices are square and either dense (i.e. full) or lower/upper triangular. Given a matrix chain of length n, we first present a dynamic programming algorithm (DPA) adapted from the well known standard algorithm and having the same O(n3) complexity. We then design and analyse two optimal O(n) greedy algorithms leading in general to different optimal solutions...

Greedy algorithms for optimal computing of matrix chain products involving square dense and triangular matrices

Faouzi Ben Charrada, Sana Ezouaoui, Zaher Mahjoub (2011)

RAIRO - Operations Research

This paper addresses a combinatorial optimization problem (COP), namely a variant of the (standard) matrix chain product (MCP) problem where the matrices are square and either dense (i.e. full) or lower/upper triangular. Given a matrix chain of length n, we first present a dynamic programming algorithm (DPA) adapted from the well known standard algorithm and having the same O(n3) complexity. We then design and analyse two optimal O(n) greedy algorithms leading in general to different optimal solutions...

G-Réseaux dans un environnement aléatoire

Jean-Michel Fourneau, Dominique Verchère (2010)

RAIRO - Operations Research

We study networks with positive and negative customers (or Generalized networks of queues and signals) in a random environment. This environment may change the arrival rates, the routing probabilities, the service rates and also the effect of signals. We prove that the steady-state distribution has a product form. This property is obtained as a corollary of a much more general result on multidimensional Markov chains.

Growth rates and average optimality in risk-sensitive Markov decision chains

Karel Sladký (2008)

Kybernetika

In this note we focus attention on characterizations of policies maximizing growth rate of expected utility, along with average of the associated certainty equivalent, in risk-sensitive Markov decision chains with finite state and action spaces. In contrast to the existing literature the problem is handled by methods of stochastic dynamic programming on condition that the transition probabilities are replaced by general nonnegative matrices. Using the block-triangular decomposition of a collection...

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