Van de Panne C. Methods for linear and quadratic programming

Amsterdam: North-Holland Publishing Company, 1975. — 500 p.This book is the outcome of a number of years of work in the area of linear and quadratic programming. Most of it is based on articles and papers
written together by Andrew Whinston or by this author only. While writing this book, I had two objectives in mind. The first one was to provide a detailed exposition of the most important methods of linear and quadratic programming which will introduce these methods to a wide variety of readers. For this purpose, numerical examples are given through out the book. The second objective was to relate the large number of methods
which exist in both linear and quadratic programming to each other. In linear programming the concepts of dual and parametric equivalence were
useful and in quadratic programming that of symmetric and asymmetric variants.
Throughout the book, the treatment is in terms of methods and tableaux resulting from these methods rather than mathematical theorems and proofs, or, in other terms, the treatment is constructive rather than analytical. The main advantage of such a constructive approach is thought to be in the accessibility of the methods. Whereas an analytical approach introduces a method through a maze of theorems after which the methods appear as an afterthought, a constructive approach first states the main principles of the method, after which obstacles and implications are dealt with one by one.
A disadvantage of detailed exposition and of numerical examples is lack of conciseness. This has resulted in the limitation of the number of topics
treated in this book. Flence such topics as decomposition methods for linear and quadratic programming, quadratic transportation problem and integer linear and quadratic programming are missing in this book, though most concepts on which methods for these problems are based follow rather naturally from the methods which are treated. However, inclusion of a number of these subjects would have increased the size of this book unduly.
The linear complementarity problem is treated in some detail, not only because it is an immediate generalization of linear and quadratic programming but also because it is amenable to an interesting generalization of the parametric methods which form the core of this book.
The book can be used for graduate or senior undergraduate courses in mathematical programming. In case of a one-year course, it could serve as
a basis for the first half; the* second half would then deal with general nonlinear programming and integer programming.