<P> In many problems, the feasible set reflects a constraint that one or more variables must be non-negative . In pure integer programming problems, the feasible set is the set of integers (or some subset thereof). In linear programming problems, the feasible set is a convex polytope: a region in multidimensional space whose boundaries are formed by hyperplanes and whose corners are vertices . </P> <P> Constraint satisfaction is the process of finding a point in the feasible region . </P> <P> A convex feasible set is one in which a line segment connecting any two feasible points goes through only other feasible points, and not through any points outside the feasible set . Convex feasible sets arise in many types of problems, including linear programming problems, and they are of particular interest because, if the problem has a convex objective function that is to be maximized, it will generally be easier to solve in the presence of a convex feasible set and any local optimum will also be a global optimum . </P> <P> If the constraints of an optimization problem are mutually contradictory, there are no points that satisfy all the constraints and thus the feasible region is the null set . In this case the problem has no solution and is said to be infeasible . </P>

What is meant by the term feasible solution space what determines this region