Approximation of Multi-Parametric Programming Problems (AMPaPro)

In parametric programming problems, the objective function and/or the feasible set depend on one or several unknown parameters. The task then consists of solving the problem for each possible combination of parameter values. For most parametric programming problems, however, specifying an optimal solution for each combination of parameter values requires an enormous number of solutions. Consequently, these problems are usually very difficult to solve exactly and the applicability of exact solution algorithms is often severely limited. This particularly holds for multi-parametric problems, where several parameters are involved. Hence, this proposal aims at developing efficient approximation methods for one- and multi-parametric programming problems that are applicable under weak assumptions and produce approximations with provably good approximation quality and small cardinality.