Numerical Optimization : Theoretical and Practical Aspects Starting with illustrative real world examples this book exposes in a tutorial way algorithms for numerical optimization: fundamental ones (Newtonian methods line searches trust region sequential quadratic programming etc.) as well as more specialized and advanced ones (nonsmooth optimization decomposition techniques and interior point methods). Most of these algorithms are explained in a detailed manner allowing straightforward implementation. Theoretical aspects are addressed with care often using minimal assumptions. The present version contains substantial changes with respect to the first edition. Part I on unconstrained optimization has been completed with a section on quadratic programming. Part II on nonsmooth optimization has been thoroughly reorganized and expanded. In addition nontrivial application problems have been inserted in the form of computational exercises. These should help the reader to get a better understanding of optimization methods beyond their abstract description by addressing important features to be taken into account when passing to implementation of any numerical algorithm. This level of detail is intended to familiarize the reader with some of the crucial questions of numerical optimization: how algorithms operate why they converge difficulties that may be encountered and their possible remedies