Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods

the long version

The concept of `reformulation' has long played an important role in mathematical programming. A classical example is the penalization technique in constrained optimization. More recent trends consist of reformulation of various mathematical programming problems, including variational inequalities and complementarity problems, into equivalent systems of possibly nonsmooth, piecewise smooth or semismooth nonlinear equations, or equivalent unconstrained optimization problems that are usually differentiable, but in general not twice differentiable. The book is a collection of peer-reviewed papers that cover such diverse areas as linear and nonlinear complementarity problems, variational inequality problems, nonsmooth equations and nonsmooth optimization problems, economic and network equilibrium problems, semidefinite programming problems, maximal monotone operator problems, and mathematical programs with equilibrium constraints. The reader will be convinced that the concept of `reformulation' provides extremely useful tools for advancing the study of mathematical programming from both theoretical and practical aspects. Audience: This book is intended for students and researchers in optimization, mathematical programming, and operations research.