Necessary conditions for an extremum, penalty functions, and regularity. (Russian) Zbl 0764.90079

Pshenichnyi, B. N.

Ukr. Mat. Zh. 44, No. 6, 805-812 (1992).

A very general concept of regularity of points related to systems of simultaneous nonlinear equations is introduced. This leads to stronger first order necessary conditions for a local minimum of nondifferentiable optimisation problems at regular points. The connection to unconstrained optimisation problems via penalty functions is also discussed.

Reviewer: E.Iwanow (Wien)

MSC:

90C30	Nonlinear programming
49J52	Nonsmooth analysis

Keywords:

generalized subgradients; regularity of points; systems of simultaneous nonlinear equations; first order necessary conditions; local minimum; nondifferentiable optimisation; penalty functions