On the properties of the feasible parametric set and its possible applications

Consider the problem of Parametric Optimization with integer variables Ps(α,β):inf{f(x,α)/x belongs to Ms(β)}. Let β,α variables from M and ¦[ respectively and let £s={β from ¦[/Ms(β) not equal to Θ} the associated feasible parametric set Mצ[ℝRk. Here some properties of the set £s are analysed, such as structure, convexity and the conditions under which it can be affirmed that £s is a closed set. The possibility of the application of this result to the Stochastic Programming Problem is also briefly discussed.