دانلود کتاب بینهایت های عددی و بی نهایت کوچک در بهینه سازی

This book is dedicated to two topics that, up to the recent times, were believed incompatible. In fact, infinities and infinitesimals for centuries were considered within highly theoretical research areas whereas optimization is a part of applied mathematics and deals with algorithms and codes implemented on computers. The possibility to join these two topics under the same cover is a consequence of the fact that infinities and infinitesimals considered here are not traditional symbolic entities but numerical ones, namely, they can be represented on a new supercomputer patented in several countries and called the Infinity Computer. This computer is able to execute numerical (i.e., floating-point) operations with numbers that can have different infinite, finite, and infinitesimal parts represented in the positional numeral system with an infinite base called grossone expressed by the numeral➀. The numerical character of these infinite and infinitesimal numbers is one of the key differences with respect to traditional theories of infinity and infinitesimals. This novel point of view opens completely new horizons not only in pure mathematics but also in computer science and applied mathematics. During the last years there was an increasing interest in this new computational paradigm. In 2013, 2016, and 2019 therewere international conferences “NUMTA—Numerical Computations: Theory and Algorithms” where the Infinity Computer and its applications were among the main topics. Several special issues in leading scientific journals have been published. The last NUMTA conference in 2019 had more than 200 participants from 30 countries. Three special issues and proceedings in volumes 11973 and 11974 of the Springer book series “Lecture Notes in Computer Science” have been published.