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CiteSeerX Scientific Literature Digital Library and Search Engine (4.232.473 recursos)

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Mostrando recursos 1 - 20 de 4.145.243


    Tyrone Rees; Martin Stoll; Andy Wathen
    The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound constraints for the control are introduced. Numerical results will illustrate the competitiveness of our techniques.


    Martin Stoll; John W. Pearson; Philip K. Maini
    The modelling of pattern formation in biological systems using various models of reaction-diffusion type has been an active research topic for many years. We here look at a parameter identification (or PDE-constrained optimization) problem where the Schnakenberg and Gierer-Meinhardt equations, two well-known pattern formation models, form the constraints to an objective function. Our main focus is on the efficient solution of the associated nonlinear programming problems via a Lagrange-Newton scheme. In particular we focus on the fast and robust solution of the resulting large linear systems, which are of saddle point form. We illustrate this by considering several two- and...

  3. Finite element error analysis for state-constrained optimal control of the Stokes equations

    J. C. De Los Reyes; C. Meyer; B. Vexler
    An optimal control problem for 2d and 3d Stokes equations is investigated with pointwise inequality constraints on the state and the control. The paper is concerned with the full discretization of the control problem allowing for different types of discretization of both the control and the state. For instance, piecewise linear and continuous approximations of the control are included in the present theory. Under certain assumptions on the L∞-error of the finite element discretization of the state, error estimates for the control are derived which can be seen to be optimal since their order of convergence coincides with the one...

  4. Sufficient optimality conditions for the Moreau-Yosida-type regularization concept applied to the semilinear elliptic optmimal control problems with pointwise state constraints

    K. Krumbiegel; I. Neitzel; A. Rösch
    We develop sufficient optimality conditions for a Moreau-Yosida regularized optimal control problem governed by a semilinear elliptic PDE with pointwise constraints on the state and the control. We make use of the equivalence of a setting of Moreau-Yosida regularization to a special setting of the virtual control concept, for which standard sec-ond order sufficient conditions have been shown. Moreover, we present a numerical example, solving a Moreau-Yosida regularized model prob-lem with an SQP method.

  5. Strategies for time-dependent PDE control with inequality constraints using an integrated modeling and simulation environment

    Ira Neitzel; UWE PRÜFERT; Thomas Slawig
    In [17] we have shown how time-dependent optimal control for partial differential equations can be realized in a modern high-level modeling and simulation package. In this article we extend our approach to (state) constrained problems. Pure state constraints in a function space setting lead to non-regular Lagrange multipliers (if they exist), i.e. the Lagrange multipliers are in general Borel measures. This will be overcome by different regularization techniques. To implement inequality constraints, active set methods and barrier meth-ods are widely in use. We show how these techniques can be realized in a modeling and simulation package. We implement a projection...

  6. Asymptotic expansion for the solution of a penalized control constrained semilinear elliptic problems

    J. Frédéric Bonnans; Francisco J. Silva


    Eduardo Casas; Fredi Tröltzsch
    A class of optimal control problems for quasilinear elliptic equations is considered, where the coefficients of the elliptic differential operator depend on the state function. First- and second-order optimality conditions are discussed for an associated control-constrained optimal control problem. Main emphasis is laid on second-order sufficient optimality conditions. To this aim, the regularity of the solutions to the state equation and its linearization is studied in detail and the Pontryagin maximum principle is derived. One of the main difficulties is the non-monotone character of the state equation.

  8. Sufficient second-order optimality conditions for semilinear control problems with pointwise state constraints

    Eduardo Casas; Juan Carlos De Los Reyes; Fredi Tröltzsch
    Second-order sufficient optimality conditions are established for the optimal control of semilinear elliptic and parabolic equations with pointwise constraints on the control and the state. In contrast to former publications on this subject, the cone of critical directions is the smallest possible in the sense that the second-order sufficient conditions are the closest to the associated necessary ones. The theory is developed for elliptic distributed controls in domains up to dimension three. Moreover, problems of elliptic boundary control and parabolic distributed control are discussed in spatial domains of dimension two and one, respectively.


    J. C. De Los Reyes; P. Merino; J. Rehberg; F. Tröltzsch
    The paper deals with optimal control problems for semilinear elliptic and parabolic PDEs subject to pointwise state constraints. The main issue is that the controls are taken from a restricted control space. In the parabolic case, they are Rm-vector-valued functions of the time, while the are vectors of Rm in elliptic problems. Under natural assumptions, first- and second-order sufficient optimality conditions are derived. The main result is the extension of second-order sufficient conditions to semilinear parabolic equations in domains of arbitrary dimension. In the elliptic case, the problems can be handled by known results of semi-infinite optimization. Here, different examples...

  10. On convergence of regularization methods for nonlinear parabolic optimal control problems with control and state constraints

    Ira Neitzel; Fredi Tröltzsch
    Moreau-Yosida and Lavrentiev type regularization methods are considered for non-linear optimal control problems governed by semilinear parabolic equations with bilateral pointwise control and state constraints. The convergence of optimal controls of the regularized problems is studied for regularization parameters tending to infinity or zero, respectively. In particular, the strong convergence of global and local solutions is addressed. Moreover, it is shown that, under cer-tain assumptions, locally optimal solutions of the Lavrentiev regularized problems are locally unique. This analysis is based on a second-order sufficient optimality condition and a separation assumption on almost active sets.


    Irwin Yousept
    An optimal control problem arising in the context of 3D electromagnetic induction heating is investigated. The state equation is given by a quasilinear stationary heat equation coupled with a semilinear timeharmonic eddy current equation. The temperature-dependent electrical conductivity and the presence of pointwise inequality state-constraints represent the main challenge of the paper. In the first part of the paper, the existence and regularity of the state are addressed. The second part of the paper deals with the analysis of the corresponding linearized equation. Some sufficient conditions are presented which guarantee the solvability of the linearized system. The final part of...

  12. Source representation strategy for optimal boundary control problems with state constraints

    F. Tröltzsch, et al.

  13. Stability of infinite dimensional control problems with pointwise state constraints

    Michael Hinze; Christian Meyer

  14. Asymptotic expansion for the solution of a penalized control constrained semilinear elliptic problems

    J. Frédéric Bonnans; Francisco J. Silva

  15. Source representation strategy for optimal boundary control problems with state constraints

    F. Tröltzsch, et al.

  16. On conditional random fields: Applications, feature selection, . . .

    Tran The Truyen

  17. Multivariate vars for operational risk capital computation: a vine structure approach

    Dominique Guégan; Bertrand K. Hassani

  18. An Autocorrelated Loss Distribution Approach: back to the time series

    Dominique Guégan; Bertrand K. Hassani
    The Advanced Measurement Approach requires financial institutions to develop internal

  19. Reconstructing posterior distributions of a species . . .

    Liang Liu
    The desire to infer the evolutionary history of a group of species should be more viable now that a considerable amount of multilocus molecular data is available. However, the current molecular phylogenetic paradigm still reconstructs gene trees to represent the species tree. Further, commonly used methods to combine data, such as the concatenation method, the consensus tree method, or the gene tree parsimony method may be biased. In this dissertation, I propose a Bayesian hierarchical model to estimate the phylogeny of a group of species using multiple estimated gene tree distributions such as those that arise in a Bayesian analysis...

  20. Extremal Matroid Theory and The Erdös-Pósa Theorem

    Kasper Kabell

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