The feasibility problem for constant scaling in output feedback control is considered. This is an inherently difficult problem since the set of feasible solutions is non-convex and may be disconnected. Nevertheless, we show that this problem can be reduced to the global minimization of a concave function over a convex set, or alternatively, to the global minimization of a convex program with an additional reverse convex constraint. Thus this feasibility problem belongs to the realm of d.c. optimization, a new field which has recently emerged as an active promising research direction in nonconvex global optimization. By exploiting the specific d.c, structure of the problem, several algorithms are proposed which at every iteration require solving only either convex or linear subproblems. Analogous algorithms with new characterizations are proposed for the bilinear matrix inequality (BMI) feasibility problem.