Selfregularity A New Paradigm For Primaldual Interiorpoint Algorithms Jiming Peng by Jiming Peng, Cornelis Roos, Tamas Terlaky 9780691091938, 0691091935 instant download after payment.

The authors deal with linear optimization, nonlinear complementarity problems, semidefinite optimization, and second-order conic optimization problems. The framework also covers large classes of linear complementarity problems and convex optimization. The algorithm considered can be interpreted as a path-following method or a potential reduction method. Starting from a primal-dual strictly feasible point, the algorithm chooses a search direction defined by some Newton-type system derived from the self-regular proximity. The iterate is then updated, with the iterates staying in a certain neighborhood of the central path until an approximate solution to the problem is found. By extensively exploring some intriguing properties of self-regular functions, the authors establish that the complexity of large-update IPMs can come arbitrarily close to the best known iteration bounds of IPMs.

Researchers and postgraduate students in all areas of linear and nonlinear optimization will find this book an important and invaluable aid to their work.