It is well-known that there are many areas of application of parametric optimization, here we merely note the fields of vector optimization (see for example W. Dinkelbach [1], J. Focke [1], J. Guddat [5], and M. Zeleny [1]) and stochastic optimization (B. Bereanu [1], [2], [5], M. M. FAber [1], R.-R. Redetzki [1], [2], and K. Tammer [7], [8], [11]). The practical exploitation of this potential however involves the need for efficient procedures for the analysis of parameter-dependent optimization problems. It is first necessary to agree on what one expects from such solution procedures. Recalling the investigations presented in the preceding chapter one could, at least for certain classes of parametric optimization problems, consider the objective of calculating a finite decomposition or partitioning of the solubility set. We will see that although achieving such a goal is conceivable it is not always necessary or indeed possible. The conditions to be met by a solution procedure may be seen as depending on
(i)
the theoretical results obtained on the structure of characteristic parameter sets of the problem and on the existence of a finite decomposition or partitioning,
(ii)
available computing technology, and
(iii)
the practical needs involved in the concrete application underlying the problem.