Hadamard well-posedness for a set-valued optimization problem

Autor:	S. J. Li, X. W. Xue, J. Zeng, W. Y. Zhang
Rok vydání:	2012
Předmět:	Set (abstract data type) Discrete mathematics Control and Optimization Optimization problem Hadamard transform Hadamard's maximal determinant problem Hadamard three-lines theorem Convergence (routing) Computational intelligence Function (mathematics) Mathematics
Zdroj:	Optimization Letters. 7:559-573
ISSN:	1862-4480 1862-4472
DOI:	10.1007/s11590-011-0439-3
Popis:	In this paper, we introduce a kind of Hadamard well-posedness for a set-valued optimization problem. By virtue of a scalarization function, we obtain some relationships between weak $${(\varepsilon, e)}$$ -minimizers of the set-valued optimization problem and $${\varepsilon}$$ -approximate solutions of a scalar optimization problem. Then, we establish a scalarization theorem of P.K. convergence for sequences of set-valued mappings. Based on these results, we also derive a sufficient condition of Hadamard well-posedness for the set-valued optimization problem.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::edc214a1a0b04d01c972755ac85979a4 https://doi.org/10.1007/s11590-011-0439-3 Zobrazit plný text záznamu Full text from SpringerLink