Regularization-robust preconditioners for time-dependent PDE constrained optimization problems

In this article, we motivate, derive and test �effective preconditioners to be used with the Minres algorithm for solving a number of saddle point systems, which arise in PDE constrained optimization problems. We consider the distributed control problem involving the heat equation with two diff�erent functionals, and the Neumann boundary control problem involving Poisson's equation and the heat equation. Crucial to the eff�ectiveness of our preconditioners in each case is an eff�ective approximation of the Schur complement of the matrix system. In each case, we state the problem being solved, propose the preconditioning approach, prove relevant eigenvalue bounds, and provide numerical results which demonstrate that our solvers are eff�ective for a wide range of regularization parameter values, as well as mesh sizes and time-steps

The Study of Optimization of Thrust Vector Control Systems

Reliability analyses and failure probabilities of S-4B stage automatic pilots and hydraulic thrust vector control system configurations, and compatibility with actuato

Using constraint preconditioners with regularized saddle-point problems

The problem of finding good preconditioners for the numerical solution of a certain important class of indefinite linear systems is considered. These systems are of a 2 by 2 block (KKT) structure in which the (2,2) block (denoted by -C) is assumed to be nonzero. In Constraint preconditioning for indefinite linear systems , SIAM J. Matrix Anal. Appl., 21 (2000), Keller, Gould and Wathen introduced the idea of using constraint preconditioners that have a specific 2 by 2 block structure for the case of C being zero. We shall give results concerning the spectrum and form of the eigenvectors when a preconditioner of the form considered by Keller, Gould and Wathen is used but the system we wish to solve may have C \neq 0 . In particular, the results presented here indicate clustering of eigenvalues and, hence, faster convergence of Krylov subspace iterative methods when the entries of C are small; such situations arise naturally in interior point methods for optimization and we present results for such problems which validate our conclusions.\ud \ud The first author's work was supported by the OUCL Doctorial Training Accoun

Fast iterative solution of reaction-diffusion control problems arising from chemical processes

PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects in our solvers are saddle point theory, mass matrix representation and effective Schur complement approximation, as well as the outer (Newton) iteration to take account of the nonlinearity of the underlying PDEs

Refined saddle-point preconditioners for discretized Stokes problems

This paper is concerned with the implementation of efficient solution algorithms for elliptic problems with constraints. We establish theory which shows that including a simple scaling within well-established block diagonal preconditioners for Stokes problems can result in significantly faster convergence when applying the preconditioned MINRES method. The codes used in the numerical studies are available online

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

Orofacial manifestations in outpatients with anorexia nervosa and bulimia nervosa focusing on the vomiting behavior

Objective: This case-control study aims to evaluate the oral health status and orofacial problems in a group of outpatients with eating disorders (ED)—either anorexia nervosa (AN) or bulimia nervosa (BN)—further focusing on the influence of vomit. Materials and methods: Fifty-five women outpatients with AN or BN diagnosis were invited to participate, of which 33 agreed. ED outpatients and matched controls were submitted to a questionnaire and clinical oral examination. Results: Multivariate analysis identified a significantly higher incidence of teeth-related complications (i.e., tooth decay, dental erosion, and self-reported dentin hypersensitivity), periodontal disease, salivary alterations (i.e., hyposalivation and xerostomia), and oral mucosa-related complications in ED outpatients. Dental erosion, self-reported dentin hypersensitivity, hyposalivation, xerostomia, and angular cheilitis were found to be highly correlated with the vomiting behavior. Conclusions: ED outpatients were found to present a higher incidence of oral-related complications and an inferior oral health status, compared to gender- and age-matched controls. Alterations verified within outpatients were acknowledged to be quite similar to those previously reported within inpatients, in both of nature and severity, thus sustaining that the cranio-maxillofacial region is significantly affected by ED, even in the early/milder forms of the condition, as expectedly verified within outpatients.The work was supported by the Faculty of Dental Medicine, U. Porto