In the past few decades, there has been a large amount of work on algorithms for linear network flow problems, special classes of network problems such as assignment problems (linear and quadratic), Steiner tree problem, topology network design and nonconvex cost network flow problems.Network optimization problems find numerous applications in transportation, in communication network design, in production and inventory planning, in facilities location and allocation, and in Vlsi design.The purpose of this book is to cover a spectrum of recent developments in network optimization problems, from linear networks to general nonconvex network flow problems Hybrid Methods for Finding the Nearest Euclidean Distance Matrix / S. Al-Homidan and R. Fletcher -- Subdifferential Characterization of Convexity / R. Correa, A. Jofre and L. Thibault -- A Simple Triangulation of R[superscript n] with Fewer Simplices for Solving Nonsmooth Convex Programming / C.-Y. Dang -- On Generalized Differentiability of Optimal Solutions and its Application to an Algorithm for Solving Bilevel Optimization Problems / S. Dempe -- Projected Gradient Methods for Nonlinear Complementarity Problems via Normal Maps / M. C. Ferris and D. Ralph -- An NCP-Function and its Use for the Solution of Complementarity Problems / A. Fischer -- An Elementary Rate of Convergence Proof for the Deep Cut Ellipsoid Algorithm / J. B. G. Frenk and J. Gromicho -- Solving Nonsmooth Equations by Means of Quasi-Newton Methods with Globalization / M. A. C. Ruggiero, J. M. Martinez and S. A. Santos Nonsmooth optimization covers the minimization or maximization of functions which do not have the differentiability properties required by classical methods. The field of nonsmooth optimization is significant, not only because of the existence of nondifferentiable functions arising directly in applications, but also because several important methods for solving difficult smooth problems lead directly to the need to solve nonsmooth problems, which are either smaller in dimension or simpler in structure.This book contains twenty five papers written by forty six authors from twenty countries in five continents. It includes papers on theory, algorithms and applications for problems with first-order nondifferentiability (the usual sense of nonsmooth optimization) second-order nondifferentiability, nonsmooth equations, nonsmooth variational inequalities and other problems related to nonsmooth optimization. This book includes papers on theory, algorithms and applications for problems with fast-order nondifferentiability, second-order nondifferentiability, nonsmooth equations, nonsmooth variational inequalities and other problems related to nonsmooth optimization.
