Other Developments in Multi‐parametric Optimization

In addition to the results on multi-parametric linear programming (mp-LP), multi-parametric quadratic programming (mp-QP), multi-parametric mixed-integer linear programming, and multi-parametric mixed-integer quadratic programming problems, there have also been interesting developments in other areas of multi-parametric programming. In many applications some parts of nonlinear programming (NLP) problem might change over time and have great impact on the solution. In order to take this into account, the uncertainty can be considered explicitly by formulating a multi-parametric-NLP (mp-NLP) problem. Arguably the most interesting algorithm for polynomial non-convex mp-NLP problems was presented by Fotiou et al. Additional approaches consider the use of a moving-front algorithm or the special case of multi-parametric dynamic optimization. Similarly to mp-LP and mp-QP problems, most solution approaches for mp-linear complementarity problems can be subdivided into two categories: geometrical and combinatorial approaches.