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Bertsekas, D. P.; Ozdaglar, A. E.

Pseudonormality and a Lagrange multiplier theory for constrained optimization. (English) Zbl 1026.90092

J. Optimization Theory Appl. 114, No. 2, 287-343 (2002).
Summary: 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 . 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.

Cited in 43 Documents

MSC:

90C46 Optimality conditions and duality in mathematical programming
49M30 Other numerical methods in calculus of variations (MSC2010)

Keywords:

pseudonormality; informative Lagrange multipliers; constraint qualifications; exact penalty functions
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References:

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