Abstract
This note presents a more general and simple proof with geometric interpretations of the equivalence of the complementarity problem to an equation (or a system of equations), given by Mangasarian in 1976. Although this fact has been used by the author and others in a different context, it is believed that it should be presented to a more general audience of optimization specialists.
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Mangasarian, O. L.,Equivalence of the Complementarity Problem to a System of Nonlinear Equations, SIAM Journal on Applied Mathematics, Vol. 31, pp. 89–92, 1976.
Rockafellar, R. T.,Augmented Lagrangian Multiplier Functions and Duality in Nonconvex Programming, SIAM Journal on Control, Vol. 12, pp. 268–285, 1974.
Wierzbicki, A. P., andKurcyusz, S.,Projection on a Cone, Penalty Functionals, and Duality Theory for Problems with Inequality Constraints in Hilbert Space, SIAM Journal on Control and Optimization, Vol. 15, pp. 25–56, 1977.
Moreau, J. J., Décomposition Orthogonale d'un Espace Hilbertien Selon, Comptes Rendus de l'Academie des Sciences de Paris, Vol. 225, pp. 238–240, 1962.
Clarke, F. H.,On the Inverse Function Theorem, Pacific Journal of Mathematics, Vol. 9, pp. 97–102, 1976.
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Communicated by O. L. Mangasarian
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Wierzbicki, A.P. Note on the equivalence of Kuhn-Tucker complementarity conditions to an equation. J Optim Theory Appl 37, 401–405 (1982). https://doi.org/10.1007/BF00935279
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DOI: https://doi.org/10.1007/BF00935279