In the present paper the dependence of a certain optimization problem on a parameter t is studied. The problem may have the form min  . As opposed to earlier papers the parameter. t in the present case runs through the whole E₁ and not through the convexity interval K₀ only. The main results are a notion of stability, which is suitable for such problems, and, associated with chis notion a partition theorem for the solvability region of this problem, which a t the same time gives the dependence of the optimal set and the solution function on the parameter t