Second Order Optimality Conditions Nonsmooth Optimization First and Second Order Directional Derivatives Riemann Type Derivatives
Issue Date:
1998
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Pliska Studia Mathematica Bulgarica, Vol. 12, No 1, (1998), 39p-50p
Abstract:
Second order sufficient and necessary conditions are given for a nonsmooth function f defined in a Banach space to attain a minimum at a point in the interior
of its domain. At the beginning sufficient conditions in terms of Riemann type derivatives are introduced. The considered examples suggest improvements to gain
more efficiency. Consequently second order conditions based on generalized Riemann type finite difference are proved and their efficiency is shown. On this ground
a generalized second order derivative is defined.
