{"product_id":"9781400825134","title":"Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms","description":"\u003cp\u003eResearch on interior-point methods (IPMs) has dominated the field of mathematical programming for the last two decades. Two contrasting approaches in the analysis and implementation of IPMs are the so-called small-update and large-update methods, although, until now, there has been a notorious gap between the theory and practical performance of these two strategies. This book comes close to bridging that gap, presenting a new framework for the theory of primal-dual IPMs based on the notion of the self-regularity of a function.\u003c\/p\u003e  \u003cp\u003eThe 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.\u003c\/p\u003e  \u003cp\u003eResearchers and postgraduate students in all areas of linear and nonlinear optimization will find this book an important and invaluable aid to their work.\u003c\/p\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":47124048576752,"sku":"9781400825134","price":85.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9781400825134_p0.jpg?v=1763712116","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9781400825134","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}