New Lagrange multipliers rules for constrained quasidifferentiable optimization
The paper contains some new first-order Lagrange multiplier rules for quasi-differentiable optimization problems with equality and inequality constraints. Let the optimization problem be given by \[ \begin{alignedat}{2} \text{minimize} &\qquad f_0(x),\\ \text{subject to} &\qquad f_i(x)\leq 0, &&\qquad i=1,\dots,m,\\ &\qquad h_j(x)=0, &&\qquad j= 1,\dots, p,\end{alignedat} \] where \(f_i,h_j: \mathbb{R}^n\to \mathbb{R}\) be quasidifferentiable functions. The author presents three necessary John type optimality conditions by means of the quasidifferentials but also by the Clarke subdifferentials of the functions using special algebraic sums and differences (in the sense of Demyanov and in the sense of Rubinov/Akhundov, respectively) of these sets. Moreover, assuming generalized convexity assumptions (generalized quasiconvexity and generalized pseudoconvexity), it is shown that the associated Kuhn-Tucker conditions are also sufficient for optimality.
necessary John type optimality conditions
scientific article; zbMATH DE number 1885676