A parametrical method for max-min nonlinear fractional problems. (English) Zbl 0532.90088

Summary: In this paper a parametrical method for solving the max-min nonlinear fractional problem is considered. The method is similar to that used in the case of the usual nonlinear fractional programming [see e.g. S. Schaible, Oper. Res. 24, 452-461 (1976; Zbl 0348.90120)] or for solving nonlinear piecewise fractional optimization problems [see the author in Math., Rev. Anal. Numer. Theor. Approximation, Anal. Numer. Theor. Approximation 4, 87-97 (1975; Zbl 0356.90056)]. In section 5 sufficient conditions for the convergence of the method are developed. For a finite approximative variant of the method, a valuation of the approximation for the optimal value is obtained. A simple class of max-min problems for which the method is finite is given.


90C32 Fractional programming
90C31 Sensitivity, stability, parametric optimization
65K05 Numerical mathematical programming methods
49M37 Numerical methods based on nonlinear programming