The minimum risk approach to special problems of mathematical programming. The distribution function of the optimal value. (English) Zbl 0567.90089

Stancu-Minasian, I. M.; Ţigan, Ştefan

Math., Rev. Anal. Numér. Théor. Approximation, Anal. Numér. Théor. Approximation 13, 175-187 (1984).

Some special classes of mathematical programming problems such as Chebyshev problems, linear plus indefinite (or fractional) programming problems are considered. For such problems the distribution function of the optimal value is determined and the minimum risk approach to them is presented. Firstly, a general model of nonlinear minimum risk problem will be discussed, followed by the treatment of the stated problems.

MSC:

90C30	Nonlinear programming
65K05	Numerical mathematical programming methods
49M37	Numerical methods based on nonlinear programming
90C32	Fractional programming

Keywords:

Chebyshev problems; distribution function of the optimal value; minimum risk approach