Performance optimization is vital in the design and operation of modern engineering systems, including communications, manufacturing, robotics, and logistics. Most engineering systems are too complicated to model, or the system parameters cannot be easily identified, so learning techniques have to be applied. This book provides a unified framework based on a sensitivity point of view. It also introduces new approaches and proposes new research topics within this sensitivity-based framework. This new perspective on a popular topic is presented by a well respected expert in the field.
It was in the middle of the 1980s, when the seminal paper by KarÂ markar opened a new epoch in nonlinear optimization. The importance of this paper, containing a new polynomial-time algorithm for linear opÂ timization problems, was not only in its complexity bound. At that time, the most surprising feature of this algorithm was that the theoretical preÂ diction of its high efficiency was supported by excellent computational results. This unusual fact dramatically changed the style and direcÂ tions of the research in nonlinear optimization. Thereafter it became more and more common that the new methods were provided with a complexity analysis, which was considered a better justification of their efficiency than computational experiments. In a new rapidly developÂ ing field, which got the name "polynomial-time interior-point methods", such a justification was obligatory. Afteralmost fifteen years of intensive research, the main results of this development started to appear in monographs [12, 14, 16, 17, 18, 19]. Approximately at that time the author was asked to prepare a new course on nonlinear optimization for graduate students. The idea was to create a course which would reflect the new developments in the field. Actually, this was a major challenge. At the time only the theory of interior-point methods for linear optimization was polished enough to be explained to students. The general theory of self-concordant functions had appeared in print only once in the form of research monograph .
This book presents the main methodological and theoretical developments in stochastic global optimization. The extensive text is divided into four chapters; the topics include the basic principles and methods of global random search, statistical inference in random search, Markovian and population-based random search methods, methods based on statistical models of multimodal functions and principles of rational decisions theory.
Key features: Inspires readers to explore various stochastic methods of global optimization by clearly explaining the main methodological principles and features of the methods; Includes a comprehensive study of probabilistic and statistical models underlying the stochastic optimization algorithms; Expands upon more sophisticated techniques including random and semi-random coverings, stratified sampling schemes, Markovian algorithms and population based algorithms; Provides a thorough description of the methods based on statistical models of objective function; Discusses criteria for evaluating efficiency of optimization algorithms and difficulties occurring in applied global optimization.
The rapidly growing interest in Chinese language teaching has not resulted
Computational Optimization: A Tribute to Olvi Mangasarian serves as an excellent reference, providing insight into some of the most challenging research issues in the field.
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