Advances in Sensitivity Analysis and Parametic Programming

the long version

The numerous advances in mathematical programming have opened up new insights about sensitivity analysis. The paradigm `What if...?' question is no longer the only question of interest. Often, we want to know `Why...?' and `Why not...?' Such questions were not analyzed in the early years of mathematical programming to the same extent that they are now, and we have not only expanded our thinking about `post-optimal analysis', but also about `solution analysis', even if the solution obtained is not optimal. Therefore, it is now time to examine all the recent advances on sensitivity analysis and parametric programming. This book combines the origins of sensitivity analysis with the state of the art. It covers much of the traditional approaches with a modern perspective, and shows recent results using the optimal partition approach, stemming from interior methods, for both linear and quadratic programming. It examines the special case of network models. It presents a neglected topic, qualitative sensitivity analysis, as well as elements of mixed integer programming and gives a modern perspective of nonlinear programming. It provides recent advances in multi-criteria mathematical programming and also describes the state-of-the-art in stochastic programming. It covers recent advances in understanding redundancy in quadratic programs, considers an approach to diagnosing infeasibility in linear and nonlinear programs, and gives an overview of sensitivity analysis for fuzzy mathematical programming.