Zyabrev, N. B. Nonlinear programming problem with decreasing cost function and the properties of its solution. (English. Russian original) Zbl 0665.90088 U.S.S.R. Comput. Math. Math. Phys. 27, No. 2, 23-29 (1987); translation from Zh. Vychisl. Mat. Mat. Fiz. 27, No. 3, 357-367 (1987). An ill-posed problem of mathematical programming with non-linear functional and non-linear constraints and decreasing cost function is defined and considered. The properties of the problem are used to reduce it to a minimum problem for a function of one variable. The reduction enables the quantitative and qualitative dependences of the solution on various input data, required for practical applications, to be studied in detail. Existence and uniqueness conditions for the solution are examined. The ranges of values of the input parameters, for which the functional has a global minimum, are found. An efficient algorithm is given for constructing the minimum of the functional and the corresponding argument. MSC: 90C30 Nonlinear programming 65K05 Numerical mathematical programming methods 49M37 Numerical methods based on nonlinear programming Keywords:ill-posed problem; non-linear functional; non-linear constraints; decreasing cost function; Existence and uniqueness conditions PDFBibTeX XMLCite \textit{N. B. Zyabrev}, U.S.S.R. Comput. Math. Math. Phys. 27, No. 2, 23--29 (1987; Zbl 0665.90088); translation from Zh. Vychisl. Mat. Mat. Fiz. 27, No. 3, 357--367 (1987) Full Text: DOI