Besides minor corrections, the present version contains substantial changes with respect to the first edition. First of all, (simplified but) nontrivial application problems have been inserted. They involve the typical operations to be performed when one is faced with a real-life application: modelling, choice of methodology and some theoretical work to motivate it, computer implementation. Such computational exercises help getting a better understanding of optimization methods beyond their theoretical description, by addressing important features to be taken into account when passing to implementation of any numerical algorithm.
In addition, the theoretical background in Part I now includes a discussion on global convergence, and a section on the classical pivotal approach to quadratic programming. Part II has been completely reorganized and expanded. The introductory chapter, on basic subdifferential calculus and duality theory, has two examples of nonsmooth functions that appear often in practice and serve as motivation (pointwise maximum and dual functions). A new section on convergence results for bundle methods has been added. The chapter on applications of nonsmooth optimization, previously focusing on decomposition of complex problems via Lagrangian duality, describes also extensions of bundle methods for handling varying dimensions, for solving constrained problems, and for solving generalized equations. Also, a brief commented review of existing software for nonlinear optimization has been added in Part III.
Finally, the reader will find additional information at http://www-rocq.inria.fr/~gilbert/bgls. The page gathers the data for running the test problems, various optimization codes, including an SQP solver (in Matlab), and pieces of software that solve the computational exercises.
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