Strong variational principles and generic well-posedness

• Autorzy: Turinici M.
• Języki publikacji: EN

Abstrakty

EN

The strong version of Ekeland's variational principle [JMAA, 47(1974), 324-353] due to Georgiev [JMAA, 131(1988), 1-21] is deductible in a direct way from the standard one. In addition, a substitution between them is possible for many generic well-posed optimization problems.

Słowa kluczowe

EN

complete metric space; lsc bounded function; logical inclusion; closed set; Hausdorff distance; denseness

PL

inkluzja logiczna; przestrzeń metryczna; funkcje ograniczone

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 4
• Strony: 935--941
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Turinici M.

• Seminarul Matematic "A. Myller", Universitatea "A. I. Cuza", 11 Copou Boulevard, 700506 Iași, Romania

Bibliografia

• [1] M. Altman, A generalization of the Brezis-Browder principle on ordered sets, Nonlinear Anal. 6 (1981), 157-165.
• [2] H. Brezis and F. E. Browder, A general principle on ordered sets in nonlinear functional analysis, Advances in Math. 21 (1976), 355-364.
• [3] A. Brondsted, On a lemma of Bishop and Phelps, Pacific J. Math. 55 (1974), 335-341.
• [4] N. Brunner, Topologische Maximalprinzipien, Z. Math. Logik Grundlag. Math. 33 (1987), 135-139.
• [5] J. Danes, Equivalence of some geometric and related results of nonlinear functional analysis, Comment. Math. Univ. Carolin. 26 (1985), 443-454.
• [6] R. Deville, G. Godefroy and V. Zizler, A smooth variational principle with applications to Hamilton-Jacobi equatons in infinite dimensions, J. Funct. Anal. 111 (1993), 197-212.
• [7] I. Ekeland, On the variational principle, J. Math. Analysis Appl. 47 (1974), 324-353.
• [8] I. Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc. (New Series) 1 (1979), 443-474.
• [9] P. G. Georgiev, The strong Ekeland variational principle, the strong drop theorem and applications, J. Math. Analysis Appl. 131 (1988), 1-21.
• [10] G. Isac, Sur l'existence de l'optimum de Pareto, Riv. Mat. Univ. Parma (Serie 4) 9 (1983), 303-325.
• [11] B. G. Kang and S. Park, On generalized ordering principles in nonlinear analysis, Nonlinear Anal. 14 (1990), 159-165.
• [12] C. Kuratowski, Topologie (vol. I), Math. Monographs vol. 20, Polish Sci. Publ., Warsaw, 1958.
• [13] R. Manka, Turinici's fixed point theorem and the Axiom of Choice, Reports Math. Logic 22 (1988), 15-19.
• [14] G. H. Moore, Zermelo's Axiom of Choice: its Origin, Development and Influence, Springer, New York, 1982.
• [15] J. P. Penot, The drop theorem, the petal theorem and Ekeland's variational principle, Nonlinear Anal. 10 (1986), 813-822.
• [16] R. R. Phelps, Convex Functions, Monotone Operators and Differentiability, Lecture Notes Math. vol. 1364, Springer, Berlin, 1989.
• [17] J. P. Revalski, Generic properties concerning well posed optimization problems, C. R. Acad. Bulgare Sci. 38 (1985), 1431.
• [18] T. Suzuki, Generalized distance and existence theorems in complete metric spaces, J. Math. Analysis Appl. 253 (2001), 440-458.
• [19] D. Tataru, Viscosity solutions of Hamilton-Jacobi equations with unbounded nonlinear terms, J. Math. Analysis Appl. 163 (1992), 345-392.
• [20] M. Turinici, A generalization of Altman's ordering principle, Proc. Arner. Math. Soc. 90 (1984), 128-132.
• [21] M. Turinici, Remarks about the drop princpile, Libertas Math., 24 (2004), 151-164.