Optimality Conditions for Quasi-Differentiable Programs with Application to Two-Level Optimization
Yo Ishizuka · SIAM Journal on Control and Optimization · 1988
As an extension of the quasi-differentiability of Demyanov et al. (V. F. Demyanov and A. M. Rubinov, Soviet Math. Dokl., 21 (1980), pp. 14–17; V. F. Demyanov and N. L. Polyakova, U.S.S.R. Comput. Math. and Math. Phys., 20 (1981), pp. 34–43), this paper introduces a new class of quasidifferentiable functions whose directional derivatives are given by a positively homogeneous function. Optimality conditions for quasi-differentiable programs are obtained by use of the generalized Farkas theorem. As an application an optimality condition is derived for an optimization problem with two-level structure.