Abstract
Image Space Analysis is reviewed and some properties of the image problem, corresponding to a given constrained extremum problem, are proved. Then, some remarks are made about optimality conditions and minimum principles.
Preview
Unable to display preview. Download preview PDF.
References
V. Dem’yanov and A. Rubinov, “Quasidifferentiability and related topics“. Kluwer, 2000
F. Giannessi, “Theorems of the alternative and optimality conditions“. Jou. Optimization Theory Appls., Vol. 42, N. 3, 1984, pp. 331–365.
F. Giannessi, “Theorems of the alternativefor multifunctions with applications to Optimization: General results“. Jou. Optimization Theory Appls., Vol. 55, N. 2, 1987, pp. 233–256.
F. Giannessi, “Sernidifferentiable functions and necessary optimality conditions“. Jou. Optimization Theory Appls., Vol. 60, N. 2, 1989, pp. 191–241.
F. Giannessi, “General optimality conditions via a separation scheme“. In ”Algorithms for continuous optimization“, E. Spedicato Ed., Kluwer Ac. Publ., 1994, pp. 1–23.
F. Giannessi, “Image space approach to Optimization“, In ”Encyclopedia of Optimization“, C.A. Floudas and P.M. Pardalos Eds., Kluwer, 2001.
F. Giannessi and A. Uderzo, “A multifunction approach to extremum problems having infinite dimensional image. I: Composition and selection“. Atti Seminario Matematico e Fisico, Università di Modena, Suppl. Vol. XLVI, 1998, pp. 771–785.
O.L. Mangasarian, “Nonlinear Programming“. SIAM, Philadelphia, 1994.
W. Oettli and M. Théra, “Equivalents of Ekeland’s principle“. Bull. Austral. Math. Sc., Vol. 48, 1993, pp. 385–392.
T. Rapcsâk, “Smooth Nonlinear Optimization in ℝ“. Kluwer, Acad. Publ., 1997.
S.M. Robinson, “Local structure of feasible sets in nonlinear programming, part III: stability and sensitivity“. Mathematical Programming Study, N. 30, 1987, pp. 45–66.
R.T. Rockafellar and R.J.-B. Wets, “Variational Analysis“. Springer-Verlag, 1998.
F. Tardella, “On the image of a constrained extremum problem and some applications to the existence of a minimum“. Jou. Optimization Theory Appls., Vol. 60, N. 1, 1989, pp. 93–104.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Kluwer Academic Publishers
About this chapter
Cite this chapter
Giannessi, F. (2001). Some Remarks on Minimum Principles. In: Hadjisavvas, N., Pardalos, P.M. (eds) Advances in Convex Analysis and Global Optimization. Nonconvex Optimization and Its Applications, vol 54. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0279-7_4
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0279-7_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-6942-4
Online ISBN: 978-1-4613-0279-7
eBook Packages: Springer Book Archive