## Well-posed optimization problems |

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### Contents

TYKHONOV WELLPOSEDNESS | 1 |

CHAPTER n HADAMARD AND TYKHONOV WELLPOSEDNESS | 38 |

GENERIC WELLPOSEDNESS | 81 |

Copyright | |

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a.e. t G A(yo arg min X arg min(X argmin assumptions Attouch Banach space bounded characterization compact consider constant Conv convex set corollary defined denote dense dense set diam dist epi-convergence example finite fixed further subsequence G arg given Hausdorff hence Hilbert space implies In(xn inf I(X Let xn lim inf lim sup linear Lipschitz continuity lower semicontinuous Lucchetti meas metric space minimizing sequence Moreover Mosco convergence multifunction nonempty obtain optimal control optimal control problem optimal solution optimal value perturbations posed posedness Proof of lemma proof of theorem Proposition proposition 21 prove reflexive Rockafellar sequence xn sequential solution Hadamard strong convergence sub lev subset sufficiently large Suppose theorem 26 Theorem Let topological trajectory uniform convergence uniformly unique upper semicontinuous variational inequality weak epi xn G yielding