2,261 research outputs found
On the Dini-Hadamard subdifferential of the difference of two functions
In this paper we first provide a general formula of inclusion for the
Dini-Hadamard epsilon-subdifferential of the difference of two functions and
show that it becomes equality in case the functions are directionally
approximately starshaped at a given point and a weak topological assumption is
fulfilled. To this end we give a useful characterization of the Dini-Hadamard
epsilon-subdifferential by means of sponges. The achieved results are employed
in the formulation of optimality conditions via the Dini-Hadamard
subdifferential for cone-constrained optimization problems having the
difference of two functions as objective.Comment: 19 page
Directed Subdifferentiable Functions and the Directed Subdifferential without Delta-Convex Structure
We show that the directed subdifferential introduced for differences of
convex (delta-convex, DC) functions by Baier and Farkhi can be constructed from
the directional derivative without using any information on the DC structure of
the function. The new definition extends to a more general class of functions,
which includes Lipschitz functions definable on o-minimal structure and
quasidifferentiable functions.Comment: 30 pages, 3 figure
ON NECESSARY CONDITIONS FOR EFFICIENCY IN DIRECTIONALLY DIFFERENTIABLE OPTIMIZATION PROBLEMS
This paper deals with multiobjective programming problems with in- equality, equality and set constraints involving Dini or Hadamard differentiable func- tions. A theorem of the alternative of Tucker type is established, and from which Kuhn-Tucker necessary conditions for local Pareto minima with positive Lagrange multipliers associated with all the components of objective functions are derived.Theorem of the alternative, Kuhn-Tucker necessary conditions, direc- tionally differentiable functions.
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