Abstract:
In this paper we introduce notions of inhomogeneous upper convex and lower concave approximations of the increment of a nonsmooth function defined in a normed space and study exhaustive families of these approximations. In terms of the introduced notions we establish optimality conditions for various constrained and unconstrained extremum problems.
Keywords:
nonsmooth analysis, inhomogeneous upper convex approximation, inhomogeneous lower concave approximation, exhaustive family of approximations, coexhauster.
This publication is cited in the following 6 articles:
Tor A.H., “An Introduction to Non-Smooth Convex Analysis Via Multiplicative Derivative”, J. Taibah Univ. Sci., 13:1 (2019), 351–359
M. E. Abbasov, “Ischislenie koekzosterov vtorogo poryadka”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 14:4 (2018), 276–285
Dolgopolik M.V., “A Convergence Analysis of the Method of Codifferential Descent”, Comput. Optim. Appl., 71:3 (2018), 879–913
M. E. Abbasov, “Second-Order Minimization Method for Nonsmooth Functions Allowing Convex Quadratic Approximations of the Augment”, J Optim Theory Appl, 171:2 (2016), 666
V. F. Demyanov, G. Sh. Tamasyan, “Direct Methods in the Parametric Moving Boundary Variational Problem”, Numerical Functional Analysis and Optimization, 35:7-9 (2014), 932
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