On a possible generalization of pshemchhy's quasidifferentiability

Abstract

Applying some results of J.-P. Cbouzeix the notion of quasidifferentiability of a function due to B. N. PSHENICHNYI is generalized and a quasisubdifferential is defined for generalized upper quasidifferentiable functions. By the help of the quasisubdifferential a necessary condition for local minima of a generalised upper qusidifferentiable function is formulated and the steepest normalizes desecent direction for a regular generalized upper quasidifferentiable function is determined.

Keywords:

• Generalized quasidifferentiability
• necessary optimality condition
• steepest descent direction
• DINI derivative

AMS 1980 Subject Classifications:

• Primary: 90 C 30
• Secondary: 26 B 25
• Secondary: 26 A 24
• Secondary: 49 D 10

¹This research was supported by the National Science Foundation of the Hungarian Academy of Sciences and Arts, Grant# OTKA 354.

¹This research was supported by the National Science Foundation of the Hungarian Academy of Sciences and Arts, Grant# OTKA 354.

Notes

¹This research was supported by the National Science Foundation of the Hungarian Academy of Sciences and Arts, Grant# OTKA 354.