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In this paper, some properties of linear functionals are studied, which are used in functional analysis, optimization theory, numerical analysis, approximation theory, various applications, etc. [ABSTRACT FROM AUTHOR]

We consider the problem of minimizing a convex linear-fractional separable function over a feasible region defined by a convex inequality constraint or linear inequality constraint, and bounds on the variables (box constraints). These problems are interesting from both theoretical and practical points of view because they arise in some mathematical programming problems and in various practical problems. Polynomial algorithms for solving such problems are proposed and their convergence is proved. Some examples and results of numerical experiments are also presented. [ABSTRACT FROM PUBLISHER]