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Some new properties of the Lagrange function and its applications. (English) Zbl 1277.90145

Summary: Using a dual problem in Wolfe type, the Lagrange function of an inequality constrained nonconvex programming problem is proved to be constant not only on its optimal solution set but also on a wider set. In addition, it is also constant on the set of Lagrange multipliers corresponding to solutions of the dual problem.

MSC:

90C46 Optimality conditions and duality in mathematical programming
49N15 Duality theory (optimization)
49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
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