Tsygankov, A. A. 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. Reviewer: Evgenij Nechaev (Moskva) MSC: 90C30 Nonlinear programming 65K05 Numerical mathematical programming methods Keywords:Lagrangian representation; existence of an extremum PDF BibTeX XML Cite \textit{A. A. Tsygankov}, Zh. Vychisl. Mat. Mat. Fiz. 44, No. 2, 242--254 (2004; Zbl 1114.90127); translation in Comput. Math. Math. Phys. 44, No. 2, 225--236 (2004) OpenURL