Abstract
We consider a class of “generalized equations,” involving point-to-set mappings, which formulate the problems of linear and nonlinear programming and of complementarity, among others. Solution sets of such generalized equations are shown to be stable under certain hypotheses; in particular a general form of the implicit function theorem is proved for such problems. An application to linear generalized equations is given at the end of the paper; this covers linear and convex quadratic programming and the positive semidefinite linear complementarity problem. The general nonlinear programming problem is treated in Part II of the paper, using the methods developed here.
Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 and by the National Science Foundation under Grant No. MCS74-20584 A02.
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© 1979 The Mathematical Programming Society
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Robinson, S.M. (1979). Generalized equations and their solutions, Part I: Basic theory. In: Huard, P. (eds) Point-to-Set Maps and Mathematical Programming. Mathematical Programming Studies, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120850
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DOI: https://doi.org/10.1007/BFb0120850
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00797-2
Online ISBN: 978-3-642-00798-9
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