Exact and fast algorithms for mixed-integer nonlinear programming (Q2802655)

The book is the printed version of the PhD thesis prepared at TU Berlin. The author discusses the exact (also in the presence of rounding errors) algorithms for mixed integer programming problems. First, the author presents the LP iterative refinement (LPIR), a new algorithm for LP with arbitrary precision assumed. The second main contribution is the development of the notion of Lagrangian variable bounds for mixed integer nonlinear programming (MINLP). The third important result consists of three new branching rules for MINLP. To be more specific, the main results of the publication are: an iterative refinement scheme for linear and quadratic programs (Chapter 2), an algorithm for exact linear and quadratic programming over the rational numbers and an algorithm to reconstruct their exact basic solutions (Chapter 3), an application of the mentioned methods to ME models from systems biology (Chapter 4), enhancements to optimization-based bound tightening that allow to improve the algorithms and use them in MINLP (Chapter 6), and the notion of minimum cover and resulting branching rules for MINLP (Chapter 7). The book covers the area of interest of many researchers. It is well written and contains new and interesting results, all of them proved with high mathematical precision. Also all the empirical experiments are well documented. I recommend this book to all the researchers interested in mixed integer programming, in particular MINLP.