The Penalty Functions Method and Multiplier Rules Based on the Mordukhovich Subdifferential
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We show that the finite-dimensional Fritz John multiplier rule, which is based on the limiting/Mordukhovich subdifferential, can be proved by using differentiable penalty functions and the basic calculus tools in variational analysis. The corresponding Kuhn–Tucker multiplier rule is derived from the Fritz John multiplier rule by imposing a constraint qualification condition or the exactness of an ℓ1 penalty function. Complementing the existing proofs, our proofs provide another viewpoint on the fundamental multiplier rules employing the Mordukhovich subdifferential.
KeywordsFinite-dimensional nondifferentiable mathematical programming problem Multiplier rule Penalty function method Mordukhovich subdifferential Basic calculus tools
AMS Subject Classifications (2000)90C47 49J52
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