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New extremum conditions for smooth problems with inequality constraints. (Russian, English) Zbl 1104.49302

Zh. Vychisl. Mat. Mat. Fiz. 42, No. 9, 1304-1315 (2002); translation in Comput. Math. Math. Phys. 42, No. 9, 1256-1267 (2002).
The method of testing of functions on the conditional extremum is offered. This method is based on usage of systems of differential equations, Gramians, functions from the minors of a matrix of partial derivatives and functions-limitations. The obtained results are correct in regular and non-regular cases.

MSC:

49J35 Existence of solutions for minimax problems
49K24 Optimal control problems with differential inclusions (nec./ suff.) (MSC2000)
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