The book introduces a groundbreaking stochastic approach to global optimization applicable in various fields such as mathematics and engineering. It addresses both constrained and unconstrained problems, offering a unified conceptual framework that enhances understanding and application of optimization techniques across disciplines.
Theory and Applications of Shannon-Wiener Information
The book delves into mathematical information theory, beginning with the Shannon-Wiener framework to quantify information through probability. It defines key concepts like message and information, progressing to countable probability spaces and Shannon entropy, illustrated through applications in statistical physics, mathematical statistics, and communication engineering. Additionally, it offers an introduction to quantum information and examines general probability spaces, emphasizing the information-theoretical analysis of dynamic systems.
Modelling and Applications of Noise Processes
Focusing on generalized stochastic processes, this textbook addresses a crucial yet overlooked area of probability theory essential for noise modeling. It serves as a comprehensive guide for both mathematicians, who seek to develop effective noise models, and engineers, who need to understand the mathematical foundations to optimally apply these models. Additionally, the book includes two appendices on probability theory and spectral theory, along with a curated set of problems and solutions, enhancing its utility for interdisciplinary collaboration.
This self-contained monograph presents a new stochastic approach to global optimization problems arising in a variety of disciplines including mathematics, operations research, engineering, and economics. The volume deals with constrained and unconstrained problems and puts a special emphasis on large scale problems. It also introduces a new unified concept for unconstrained, constrained, vector, and stochastic global optimization problems. All methods presented are illustrated by various examples. Practical numerical algorithms are given and analyzed in detail. The topics presented include the randomized curve of steepest descent, the randomized curve of dominated points, the semi-implicit Euler method, the penalty approach, and active set strategies. The optimal decoding of block codes in digital communications is worked out as a case study and shows the potential and high practical relevance of this new approach. Global Optimization: A Stochastic Approach is an elegant account of a refined theory, suitable for researchers and graduate students interested in global optimization and its applications.