Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization

Interior point methods provide an attractive class of approaches for solving linear, quadratic and nonlinear programming problems, due to their excellent efficiency and wide applicability. In this paper, we consider PDE-constrained optimization problems with bound constraints on the state and control variables, and their representation on the discrete level as quadratic programming problems. To tackle complex problems and achieve high accuracy in the solution, one is required to solve matrix systems of huge scale resulting from Newton iteration, and hence fast and robust methods for these systems are required. We present preconditioned iterative techniques for solving a number of these problems using Krylov subspace methods, considering in what circumstances one may predict rapid convergence of the solvers in theory, as well as the solutions observed from practical computations

On Block Triangular Preconditioners for the Interior Point Solution of PDE-Constrained Optimization Problems

We consider the numerical solution of saddle point systems of equations resulting from the discretization of PDE-constrained optimization problems, with additional bound constraints on the state and control variables, using an interior point method. In particular, we derive a Bramble-Pasciak Conjugate Gradient method and a tailored block triangular preconditioner which may be applied within it. Crucial to the usage of the preconditioner are carefully chosen approximations of the (1,1)-block and Schur complement of the saddle point system. To apply the inverse of the Schur complement approximation, which is computationally the most expensive part of the preconditioner, one may then utilize methods such as multigrid or domain decomposition to handle individual sub-blocks of the matrix system

Homeostatic regulation of the endoneurial microenvironment during development, aging and in response to trauma, disease and toxic insult

The endoneurial microenvironment, delimited by the endothelium of endoneurial vessels and a multi-layered ensheathing perineurium, is a specialized milieu intérieur within which axons, associated Schwann cells and other resident cells of peripheral nerves function. The endothelium and perineurium restricts as well as regulates exchange of material between the endoneurial microenvironment and the surrounding extracellular space and thus is more appropriately described as a blood–nerve interface (BNI) rather than a blood–nerve barrier (BNB). Input to and output from the endoneurial microenvironment occurs via blood–nerve exchange and convective endoneurial fluid flow driven by a proximo-distal hydrostatic pressure gradient. The independent regulation of the endothelial and perineurial components of the BNI during development, aging and in response to trauma is consistent with homeostatic regulation of the endoneurial microenvironment. Pathophysiological alterations of the endoneurium in experimental allergic neuritis (EAN), and diabetic and lead neuropathy are considered to be perturbations of endoneurial homeostasis. The interactions of Schwann cells, axons, macrophages, and mast cells via cell–cell and cell–matrix signaling regulate the permeability of this interface. A greater knowledge of the dynamic nature of tight junctions and the factors that induce and/or modulate these key elements of the BNI will increase our understanding of peripheral nerve disorders as well as stimulate the development of therapeutic strategies to treat these disorders

Decision Aid Tools for the Preservation of Fruits by Modified Atmosphere Packaging

Modified atmosphere packaging (MAP) is commonly used for packing fruits and relies on the natural interplay between the produce physiology (consumption or production of gases and vapours) and the mass transfer properties of the packaging material (gases and vapours permeation values), with possible gas flushing, in order to reach optimal conditions of storage. Then success of MAP depends on the choice of the material, whose mass transfer properties must match produce requirements. Decision aid tool for MAP of fruits would aim at helping decision makers to find the best material for a given fruit, but are not yet well developed and commonly used. If virtual MAP models exist, their objective is to dimension gas permeabilities of the packaging material to the needs of the fruit. They do not take into account multi-criteria design such as cost and mechanical properties. Then, this chapter brings an overview on current researches and developments in the field of biological, material, and computing science that could lead to the development of such a tool in regard to constitution of databases, and reliability of optimization and interrogation procedures