Fractional programming
The objective function in a fractional program is a ratio of two functions that are in general nonlinear.The ratio to be optimized often describes some kind of efficiency of a system.be real-valued functions defined on a set, is called a fractional program.A fractional program in which f is nonnegative and concave, g is positive and convex, and S is a convex set is called a concave fractional program.If g is affine, f does not have to be restricted in sign.The linear fractional program is a special case of a concave fractional program where all functionsis semistrictly quasiconcave on S. If f and g are differentiable, then q is pseudoconcave.In a linear fractional program, the objective function is pseudolinear., any concave fractional program can be transformed to the equivalent parameter-free concave program[1] If g is affine, the first constraint is changed toand the assumption that g is positive may be dropped.The Lagrangian dual of the equivalent concave program is