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Computable numerical bounds for lagrange multipliers of stationary points of non-convex differentiable non-linear programs
Authors:OL Mangasarian
Institution:Computer Sciences Department, University of Wisconsin, Madison, WI 53706, USA
Abstract:It is shown that the satisfaction of a standard constraint qualification of mathematical programming 5] at a stationary point of a non-convex differentiable non-linear 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 ≧ 1.
Keywords:non-linear programming  Lagrange multipliers
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