Computable numerical bounds for Lagrange multipliers of stationary points of nonconvex differentiable nonlinear programs (Q1058992)

It is shown that the satisfaction of a standard constraint qualification of mathematical programming at a stationary point of a nonconvex differentiable nonlinear program provides explicit numerical bounds for the set of all Lagrange multipliers associated with the stationary point. Solution of a single linear program gives a sharper bound together with an achievable bound on the 1-norm of the multipliers associated with the inequality constraints. The simplicity of obtaining these bounds contrasts sharply with the intractable NP-complete problem of computing an achievable upper bound on the p-norm of the multipliers associated with the equality constraints for integer \(p\geq 1\).