  The motivation of this paper is the development of an optimisation method for
solving optimisation problems appearing in Chebyshev rational and generalised
rational approximation problems, where the approximations are constructed as
ratios of linear forms (linear combinations of basis functions). The
coefficients of the linear forms are subject to optimisation and the basis
functions are continuous function. It is known that the objective functions in
generalised rational approximation problems are quasi-convex. In this paper we
also prove a stronger result, the objective functions are pseudo-convex in the
sense of Penot and Quang. Then we develop numerical methods, that are efficient
for a wide range of pseudo-convex functions and test them on generalised
rational approximation problems.
