Second-order conditions in extremal problems. The abnormal points. (English) Zbl 0922.49017
The author considers minimization problems in finite-dimensional space with constraints for the abnormal case, i.e., when the Lagrange multiplier rule is fulfilled for an arbitrary goal functional and bears no information. Under suitable conditions new first- and second-order informative necessary as well as sufficient conditions for a minimum are obtained. The results are compared with well-known ones in this field and it is shown that those presented in the paper generalize them. A special class of constraints (so called 2-normal constraints) are derived and it is shown that for them the gap between the sufficient and the necessary conditions is as minimal as possible. It is proved that 2-normal constraint is generic.
Reviewer: E.G.Al’brekht (Ekaterinburg)
MSC:
| 49K27 | Optimality conditions for problems in abstract spaces |
Keywords:
minimization; the Lagrange multiplier rule; singularity; first- and second-order informative necessary conditionsCitations:
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