SENSITIVITY ANALYSIS OF OPTIMAL VALUE-FUNCTIONS OF CONVEX PARAMETRIC PROGRAMS WITH POSSIBLY EMPTY SOLUTION SETS

Let g(y(1), y(2)) be the optimal value of the abstract program which c onsists in minimizing a convex function f : X --> R boolean OR {+infin ity} over a feasible set of the form {x is an element of X : A(1)x = y (1), A(2)x less than or equal to(K) y(2)}. Without assuming the existe nce of optimal solutions to this minimization problem, we derive formu las for the subdifferential and the approximate subdifferential of g. Several applications are discussed.