Screen LibraryOptimization and differentiation /
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| Main Authors: | |
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| Published: |
CRC Press, Taylor & Francis Group,
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| Publisher Address: | Boca Raton, FL : |
| Publication Dates: | [2018] |
| Literature type: | Book |
| Language: | English |
| Series: |
Monographs and research notes in mathematics. |
| Subjects: | |
| Item Description: | "A Chapman & Hall book." |
| Carrier Form: | xxi, 515 pages : illustrations ; 24 cm. |
| Bibliography: | Includes bibliographical references (pages 473-510) and index. |
| ISBN: |
9781498750936 1498750931 |
| Index Number: | QA402 |
| CLC: | O224 |
| Call Number: | O224/S486 |
| Contents: |
Machine generated contents note: Necessary conditions of extremum for functionals -- Minimization of functions and stationary condition -- Lagrange problem and Euler equation -- Linear spaces -- Linear normalized spaces -- Directional differentiation -- Gateaux differentiation of functionals -- Minimization of functionals and stationary condition -- General functional spaces -- Minimization of Dirichlet integral -- Minimization of functionals on subspaces -- Derivatives with respect to subspaces -- Minimization of functionals on affine varieties -- Minimization of functionals on convex sets -- Comments -- Minimization of functionals. Addition -- Sufficiency of extremum conditions -- Existence of the function minimum -- Weak convergence in Banach spaces -- Existence of the functional minimum -- Uniqueness of the functional minimum -- Tihonov well-posedness of extremum problems -- Hadamard well-posedness of extremum problems -- Ekeland principle and the approximate condition of extremum -- Non-smooth functionals and subdifferentiation -- Frechet differentiation of functionals -- Approximate methods of functionals minimization -- Linear systems -- Additional results of functional analysis -- Abstract linear control systems -- Dirichlet problem for the Poisson equation -- Optimal control problem statement -- Necessary conditions of optimality -- Optimal control problems with local constraints -- Lagrange multipliers method -- Maximum principle -- Penalty method -- Additional properties of Sobolev spaces -- Nonhomogeneous Dirichlet problem for the elliptic equation -- Weakly nonlinear systems -- Differentiation of operators -- Inverse function theorem -- Optimal control problems for weakly nonlinear systems -- Equations with monotone operators -- Additional results of the functional analysis -- Nonlinear elliptic equation -- Optimal control problems for nonlinear elliptic equations -- Optimal control problems for general functionals -- Optimal control problems for semilinear elliptic equations -- Differentiation of the inverse operator -- Strongly nonlinear systems -- Introduction -- Absence of the differentiability of the inverse operator -- Extended differentiation of operators -- Necessary conditions of optimality for the strongly nonlinear system -- Boundary control for Neumann problem -- Extended differentiability of the inverse operator -- Coefficients optimization control problems -- Coefficients control problem -- Derivative with respect to a convex set -- Optimization control problem for bilinear systems -- Analysis of the coefficient optimization problem -- Nonlinear system with the control at the coefficients -- Differentiability with respect to a convex set for abstract systems -- Strongly nonlinear systems with the control at the coefficients -- Systems with nonlinear control -- Implicit function theorem -- Optimization control problems for abstract systems -- Weakly nonlinear control systems -- Extended differentiability of the implicit function -- Strongly nonlinear control systems -- Linear first-order evolution systems -- Abstract functions -- Ordinary differential equations -- Linear first order evolutional equations -- Optimization control problems for linear evolutional equations -- Optimization control problems for the heat equation -- Optimization control problems with the functional that is not dependent from the control -- Non-conditional optimization control problems -- Non-conditional optimization control problems for the heat equation -- Hamilton-Jacobi equation -- Hellman method for an optimization problem for the heat equation -- Nonlinear first order evolutional systems -- Nonlinear evolutional equations with monotone operators -- Optimization control problems for evolutional equations with monotone operator -- Optimization control problems for the nonlinear heat equation -- Necessary optimality conditions for the nonlinear heat equation -- Optimization control problems with the functional that is not dependent upon the control -- Sufficient optimality conditions for the nonlinear heat equation -- Coefficient optimization problems for linear parabolic equations -- Coefficient optimiz |