Pseudonormality and a Lagrange Multiplier Theory for Constrained Optimization

D.P. Bertsekas and A.E. Ozdaglar
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D.P. Bertsekas: Massachusetts Institute of Technology
A.E. Ozdaglar: Massachusetts Institute of Technology

Journal of Optimization Theory and Applications, 2002, vol. 114, issue 2, No 3, 287-343

Abstract: Abstract We consider optimization problems with equality, inequality, and abstract set constraints, and we explore various characteristics of the constraint set that imply the existence of Lagrange multipliers. We prove a generalized version of the Fritz–John theorem, and we introduce new and general conditions that extend and unify the major constraint qualifications. Among these conditions, two new properties, pseudonormality and quasinormality, emerge as central within the taxonomy of interesting constraint characteristics. In the case where there is no abstract set constraint, these properties provide the connecting link between the classical constraint qualifications and two distinct pathways to the existence of Lagrange multipliers: one involving the notion of quasiregularity and the Farkas lemma, and the other involving the use of exact penalty functions. The second pathway also applies in the general case where there is an abstract set constraint.

Keywords: pseudonormality; informative Lagrange multipliers; constraint qualifications; exact penalty functions (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (13)

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DOI: 10.1023/A:1016083601322

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