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On the quadratic form structure in a mathematical programming problem. (Russian, English) Zbl 1114.90127

Zh. Vychisl. Mat. Mat. Fiz. 44, No. 2, 242-254 (2004); translation in Comput. Math. Math. Phys. 44, No. 2, 225-236 (2004).
By introducing special functions the values of which at stationary points coincide with the values of the Lagrange multipliers, it is shown that a quadratic form that is an analogue of the quadratic form used in the well-known Lagrange method can be represented as a difference of two products, with one of the factors in each product being a nonnegative function. Based on this representation, sufficient conditions for the existence of an extremum are obtained. The conditions are valid for both regular and irregular (degenerate) cases.

MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
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