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.


90C30 Nonlinear programming
65K05 Numerical mathematical programming methods