## Large-Scale Optimization with Applications: Part I: Optimization in Inverse Problems and DesignInverse problems and optimal design have come of age as a consequence of the availability of better, more accurate, and more efficient simulation packages. Many of these simulators, which can run on small workstations, can capture the complicated behavior of the physical systems they are modeling, and have become commonplace tools in engineering and science. There is a great desire to use them as part of a process by which measured field data are analyzed or by which design of a product is automated. A major obstacle in doing precisely this is that one is ultimately confronted with a large-scale optimization problem. This volume contains expository articles on both inverse problems and design problems formulated as optimization. Each paper describes the physical problem in some detail and is meant to be accessible to researchers in optimization as well as those who work in applied areas where optimization is a key tool. What emerges in the presentations is that there are features about the problem that must be taken into account in posing the objective function, and in choosing an optimization strategy. In particular there are certain structures peculiar to the problems that deserve special treatment, and there is ample opportunity for parallel computation. THIS IS BACK COVER TEXT!!! Inverse problems and optimal design have come of age as a consequence of the availability of better, more accurate, and more efficient, simulation packages. The problem of determining the parameters of a physical system from |

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### Contents

SPACE MAPPING OPTIMIZATION FOR ENGINEERING DESIGN | 1 |

THE IDENTIFICATION OF THE CURRENT DENSITY PROFILE IN A TOKAMAK | 17 |

DUALITY FOR INVERSE PROBLEMS IN WAVE PROPAGATION | 37 |

PIECEWISE DIFFERENTIABLE MINIMIZATION FOR ILLPOSED INVERSE PROBLEMS | 63 |

THE USE OF OPTIMIZATION IN THE RECONSTRUCTION OF OBSTACLES FROM ACOUSTIC OR ELECTROMAGNETIC SCATTERING DATA | 81 |

DESIGN OF 3DREPLECTORS FOR NEAR FIELD AND FAR FIELD PROBLEMS | 101 |

OPTIMAL DIE SHAPE AND RAM VELOCITY DESIGN FOR METAL FORGING | 119 |

EIGENVALUES IN OPTIMUM STRUCTURAL DESIGN | 135 |

OPTIMIZATION ISSUES IN OCEAN ACOUSTICS | 151 |

GRADIENT METHODS IN INVERSE ACOUSTIC AND ELECTROMAGNETIC SCATTERING | 173 |

ATMOSPHERIC DATA ASSIMILATION BASED ON THE REDUCED HESSIAN SUCCESSIVE QUADRATIC PROGRAMMING ALGORITHM | 195 |

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4DVAR problems affine scaling Newton algorithm approach approximation assume B-Spline coefficients computational consider constrained optimization constraint contrast convergence cost functional defined denotes density descent direction determine dimensional direct problem discretized domain Dual space efficient electromagnetic equation example field problem Figure finite flux forging formulation frequency global gradient method IEEE ill-posed illuminated plane integral inverse problem IRLS Lagrange multiplier Large-Scale Optimization least squares linear magnetic matched field Mathematics matrix measurements modified gradient multi-experiment Newton method nonlinear numerical objective function obstacle obtained Ocean acoustic tomography optimization problem parameters perturbation piecewise differentiable plane wave plane wave detection plasma quadratic ram velocity reconstruction reduced Hessian reflector Santosa scattering problem Section seismic shape SIAM simulated solution solve sound-speed profile Space Mapping steepest descent structural subregion surface symmetric matrix technique Theory Tikhonov regularization tion Tokamak tomography total variation unconstrained updated values vector wave propagation