Second Order Optimality Conditions in Nonsmooth Unconstrained Optimization
Second Order Optimality Conditions in Nonsmooth Unconstrained Optimization
Summary: Second order necessary and sufficient 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.
- Institute of Mathematics and Informatics Bulgaria
- Bulgarian Academy of Sciences Bulgaria
- University of Insubria Italy
- Università dell Insubria (Varese) Italy
Riemann type derivatives, Nonsmooth Optimization, Nonlinear programming, first and second order directional derivatives, Second Order Optimality Conditions, Riemann Type Derivatives, Nonsmooth analysis, First and Second Order Directional Derivatives, Optimality conditions for problems in abstract spaces, nonsmooth optimization, second order optimality conditions
Riemann type derivatives, Nonsmooth Optimization, Nonlinear programming, first and second order directional derivatives, Second Order Optimality Conditions, Riemann Type Derivatives, Nonsmooth analysis, First and Second Order Directional Derivatives, Optimality conditions for problems in abstract spaces, nonsmooth optimization, second order optimality conditions
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!