Existence of solutions in parametric optimization and porosity

• Autorzy: Zaslavski A. J.
• Języki publikacji: EN

Abstrakty

EN

In this work we study the parametric family of the minimization problems f (b, x) → min, x ∈ X on a complete metric space X with a parameter b which belongs to a Hausdorff compact space Β. Here f(•,•) belongs to a space of functions on Β x X, say Μ, endowed with an appropriate metric. We study the set of all functions f(•,•) ∈ Μ for which the corresponding parametric family of the minimization problems has solutions for all parameters b ∈ Β. We show that the complement of this set is not only of the first category but also a σ-porous set. This result and its extensions are obtained as realizations of a variational principle.

Słowa kluczowe

EN

compact sets; parametric optimization; porous sets; metric space

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2006
• Tom: Vol. 28
• Strony: 161--184
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Zaslavski A. J.

• Department of Mathematics Technion-Israel Institute of Technology 32000, Haifa, Israel,

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