## Optimization on Metric and Normed Spaces"Optimization on Metric and Normed Spaces" is devoted to the recent progress in optimization on Banach spaces and complete metric spaces. Optimization problems are usually considered on metric spaces satisfying certain compactness assumptions which guarantee the existence of solutions and convergence of algorithms. This book considers spaces that do not satisfy such compactness assumptions. In order to overcome these difficulties, the book uses the Baire category approach and considers approximate solutions. Therefore, it presents a number of new results concerning penalty methods in constrained optimization, existence of solutions in parametric optimization, well-posedness of vector minimization problems, and many other results obtained in the last ten years. The book is intended for mathematicians interested in optimization and applied functional analysis. |

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### Contents

1 | |

11 | |

3 Stability of the Exact Penalty | 81 |

4 Generic WellPosedness of Minimization Problems | 121 |

5 WellPosedness and Porosity | 181 |

6 Parametric Optimization | 225 |

7 Optimization with Increasing Objective Functions | 266 |

8 Generic WellPosedness of Minimization Problems with Constraints | 311 |

9 Vector Optimization | 348 |

10 Infinite Horizon Problems | 395 |

427 | |

432 | |

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assume without loss Banach space bounded subsets closed subset compact complete metric space completes the proof continuous functions converges convex countable intersection critical point deﬁnition Denote E G X easy everywhere dense subsets exact penalty exists a neighborhood exists a positive exists a set f G A f G M ﬁnite ﬁnite-valued following assertion holds following property holds functions f G A1 g inf(g G R1 G X satisfying inequality implies inf(f inf{f(z intersection of open Lemma Let 6 G Let f lower semicontinuous lower semicontinuous functions minimal element minimization problem minimize natural number norm o-porous optimization positive number proof of Theorem property P1 Proposition real number satisﬁes strong topology strongly well-posed topology induced uniformity determined unique solution variational principle weak topology well-posed with respect x G X X I R1