ИСТИНА

We discuss possible scenarios of dual behaviour of Newton-type methods when applied to constrained optimization problems with nonunique multipliers associated to a solution. Among those scenarios are (a) failure of convergence of the dual sequence; (b) convergence to a so-called critical multiplier (which, in particular, violates the second-order sufficient condition for optimality), which appears to be a typical scenario when critical multiplier exists; (c) convergence to a noncritical multiplier. The case of mathematical programs with complementarity constraints is also discussed.