## Numerical Methods in Sensitivity Analysis and Shape OptimizationSensitivity analysis and optimal shape design are key issues in engineering that have been affected by advances in numerical tools currently available. This book, and its supplementary online files, presents basic optimization techniques that can be used to compute the sensitivity of a given design to local change, or to improve its performance by local optimization of these data. The relevance and scope of these techniques have improved dramatically in recent years because of progress in discretization strategies, optimization algorithms, automatic differentiation, software availability, and the power of personal computers. Numerical Methods in Sensitivity Analysis and Shape Optimization will be of interest to graduate students involved in mathematical modeling and simulation, as well as engineers and researchers in applied mathematics looking for an up-to-date introduction to optimization techniques, sensitivity analysis, and optimal design. |

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### Contents

Finite Dimensional Optimization | 25 |

Newtons Algorithms | 35 |

Constrained Optimization | 53 |

Copyright | |

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### Common terms and phrases

adjoint mode adjoint state equation admissible designs aeroelastic approximation automatic differentiation boundary calculation Chapter computational grid computing the gradient configuration constrained optimization construction control parameters convergence corresponding cost function cubic spline curve defined deflection delyccl denotes design constraints design parameters direction of descent directional derivatives discretization domain dot product double precision enddo equality constraints Euler-Lagrange equations Figure fluid gi(zk given global GMRES GMRES algorithm Hessian hi(z inequality constraints initial input integer interior point algorithm interior point method introduced iteration Jacobian Lagrange multipliers Lagrangian line search line search strategy linear system matrix mesh deformation minimization problem Newton Newton's algorithm nodes notation nseg obtained Odyssee optimality conditions output Parameter number preslccl REAL residual respect sensitivity analysis shape optimization solution solver spline interpolation srOls step structure subroutine subroutine computing tangent techniques theorem update variables variants vector Vj(z X_(z