Maximal and Variational Principles in Vector Spaces

Mihai Turinici ()
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Mihai Turinici: “A. I. Cuza” University, “A. Myller” Mathematical Seminar

A chapter in Computation, Cryptography, and Network Security, 2015, pp 525-575 from Springer

Abstract: Abstract In Sect. 1, a separable type extension of Ekeland’s variational principle (J Math Anal Appl 47:324–353, 1974) is given, in the realm of ordered convergence spaces. The connections with a related statement in Khanh (Bull Acad Pol Sci (Math) 37:33–39, 1989) are then discussed. In Sect. 2, the Brezis–Browder ordering principle (Adv Math 21:355–364, 1976) is used to establish a lot of maximality results in triangular structures due to Pasicki (Nonlinear Anal 74:5678–5684, 2011). Finally, in Sect. 3, some technical aspects of the variational principle due to Bao and Mordukhovich (Control Cyb 36:531–562, 2007) are being analyzed. Further, an extension of this result is proposed, by means of a pseudometric maximal principle in Turinici (Note Mat 28:33–41, 2008).

Keywords: Metric space; Completeness; Ekeland variational principle; Vector space; Convex cone; Separable property; Convergence structure; Ordering; Vector half-metric; Maximal/minimal element; Dependent choice principle; Triangular map; Strong almost completeness; Transitive brezis-browder principle; Domination property; Level-set mapping; Properness; Admissible point (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-18275-9_23

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