This book provides a friendly introduction to the paradigm and proposes a broad panorama of killing applications of the Infinity Computer in optimization: radically new numerical algorithms, great theoretical insights, efficient software implementations, and interesting practical case studies. This is the first book presenting to the readers interested in optimization the advantages of a recently introduced supercomputing paradigm that allows to numerically work with different infinities and infinitesimals on the Infinity Computer patented in several countries. One of the editors of the book is the creator of the Infinity Computer, and another editor was the first who has started to use it in optimization. Their results were awarded by numerous scientific prizes. This engaging book opens new horizons for researchers, engineers, professors, and students with interests in supercomputing paradigms, optimization, decision making, game theory, and foundations of mathematics and computer science. “Mathematicians have never been comfortable handling infinities... But an entirely new type of mathematics looks set to by-pass the problem... Today, Yaroslav Sergeyev, a mathematician at the University of Calabria in Italy solves this problem... ” MIT Technology Review “These ideas and future hardware prototypes may be productive in all fields of science where infinite and infinitesimal numbers (derivatives, integrals, series, fractals) are used.” A. Adamatzky, Editor-in-Chief of the International Journal of Unconventional Computing. “I am sure that the new approach ... will have a very deep impact both on Mathematics and Computer Science.” D. Trigiante, Computational Management Science. “Within the grossone framework, it becomes feasible to deal computationally with infinite quantities, in a way that is both new (in the sense that previously intractable problems become amenable to computation) and natural”. R. Gangle, G. Caterina, F. Tohmé, Soft Computing. “The computational features offered by the Infinity Computer allow us to dynamically change the accuracy of representation and floating-point operations during the flow of a computation. When suitably implemented, this possibility turns out to be particularly advantageous when solving ill-conditioned problems. In fact, compared with a standard multi-precision arithmetic, here the accuracy is improved only when needed, thus not affecting that much the overall computational effort.” P. Amodio, L. Brugnano, F. Iavernaro & F. Mazzia, Soft Computing

This book constitutes the refereed proceedings of the 22nd International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2023, held in Ekaterinburg, Russia, during July 2–8, 2023. The 28 full papers and 1 short paper included in this book were carefully reviewed and selected from 89 submissions. They were organized in topical sections as follows: Mathematical programming and applications; discrete and combinatorial optimization; stochastic optimization; scheduling; game theory; and optimal control and mathematical economics. The book also contains one invited talk in full paper length.

This book constitutes the proceedings of the 21st International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2022, held in Petrozavodsk, Russia, in July 2022. The 21 full papers presented together with 6 invited abstracts lectures and 2 tutorial abstracts in this volume were carefully reviewed and selected from 88 submissions. The conference focuses on the following topics: Mathematical programming, bi-level and global optimization, integer programming and combinatorial optimization, approximation algorithms with theoretical guarantees and approximation schemes, heuristics and meta-heuristics, game theory, optimal control, optimization in machine learning and data analysis, and their valuable applications in operations research and economics.

This book provides a friendly introduction to the paradigm and proposes a broad panorama of killing applications of the Infinity Computer in optimization: radically new numerical algorithms, great theoretical insights, efficient software implementations, and interesting practical case studies. This is the first book presenting to the readers interested in optimization the advantages of a recently introduced supercomputing paradigm that allows to numerically work with different infinities and infinitesimals on the Infinity Computer patented in several countries. One of the editors of the book is the creator of the Infinity Computer, and another editor was the first who has started to use it in optimization. Their results were awarded by numerous scientific prizes. This engaging book opens new horizons for researchers, engineers, professors, and students with interests in supercomputing paradigms, optimization, decision making, game theory, and foundations of mathematics and computer science.

This book constitutes the refereed proceedings of the 16th International Conference on Learning and Intelligent Optimization, LION 16, which took place in Milos Island, Greece, in June 2022. The 36 full papers and 3 short papers presented in this volume were carefully reviewed and selected from 60 submissions. LION deals with automatic solver configuration, parallel methods, intelligent optimization, nature-inspired algorithms, hard combinatorial optimization problems, DC learning, computational intelligence, and others. The contributions were organized in topical sections as follows: Invited Papers; Contributed Papers.

The two-volume set LNCS 11973 and 11974 constitute revised selected papers from the Third International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2019, held in Crotone, Italy, in June 2019. This volume, LNCS 11974, consists of 19 full and 32 short papers chosen among regular papers presented at the the Conference including also the paper of the winner (Lorenzo Fiaschi, Pisa, Italy) of The Springer Young Researcher Prize for the best NUMTA 2019 presentation made by a young scientist. The papers in part II explore the advanced research developments in such interconnected fields as local and global optimization, machine learning, approximation, and differential equations. A special focus is given to advanced ideas related to methods and applications using emerging computational paradigms.

This book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. This new edition contains computational exercises in the form of case studies which help understanding optimization methods beyond their theoretical description when coming to actual implementation.