Parallel Computations in Global Optimization Problems

This paper is devoted to the analysis of complex multi-extremal models of decision-making, which is traditional for Professor R.G. Strongin’s world-renown scientific school in this field. The work contains the necessary theoretical apparatus for constructing and analyzing parallel methods based on the information-statistical approach to constructing optimization methods, the characteristic theory of convergence and the effectiveness of methods for finding the extremum, and the methodology for reducing the complexity of models under examination. It gives a description of computational schemes of optimization methods, their theoretical justification and examples of practical application. It provides a brief depiction of the software that realizes, in the form of complete software systems, the proposed methods for searching for globally optimal solutions and has found its application in solving complex applied problems and in the learning process as a medium for performing laboratory work and research. The book is intended for a wide range of students, graduate students and professionals who want to study and practically use parallel methods of global optimization for solving computationally labor-intensive applied problems. The Academic Council of the Faculty of Computational Mathematics and Cybernetics (CMC), Lobachevsky Nizhny Novgorod State University recommends this monograph for use in the educational process. The monograph was prepared as part of the project of the Presidential Commission on Modernization and Technological Development of the Russian Economy ‘Creating a System for Training Highly Qualified Personnel in the Field of Supercomputer Technologies and Specialized Software.’