Computable Numerical Bounds for Lagrange Multipliers of Stationary Points of Nonconvex Differentiable Nonlinear Programs.

Abstract

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 > or = 1. Keywords: Nonlinear programming, Lagrange multipliers.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1985
Accession Number
ADA153513

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  • Olvi L. Mangasarian

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  • University of Wisconsin–Madison

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  • Applied Mathematics
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  • Mathematics

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