ИСТИНА

It is known that when the set of Lagrange multipliers associated with a stationary point of a constrained optimization problem is not a singleton, this set may contain some special instances so-called critical multipliers. This special subset of Lagrange multipliers denes, to a great extent, the stability pattern of solution in question subject to parametric perturbations, and the behavior of Newton-type methods. Criticality of a Lagrange multiplier can be equivalently characterized by the absence of the local Lipschitzian error bound in terms of the natural residual of the optimality system, and this view of criticality served as a basis for a recent extension of the concept of criticality to solutions of general nonlinear equations (not necessarily with primal-dual optimality structure). Here we discuss some possibilities of at least partial further extension of these results to the case of constrained equations, which is a very rich problem setting encompassing a much wider area of applications than the unconstrained case.