Initial training in pure and applied sciences tends to present problem-solving as the process of elaborating explicit closed-form solutions from basic principles, and then using these solutions in numerical applications. This approach is only applicable to very limited classes of problems that are simple enough for such closed-form solutions to exist. Unfortunately, most real-life problems are too complex to be amenable to this type of treatment.Numerical Methods - a Consumer Guide presents methods for dealing with them.
Shifting the paradigm from formal calculus to numerical computation, the text makes it possible for the reader to
Â· discover how to escape the dictatorship of those particular cases that are simple enough to receive a closed-form solution, and thus gain the ability to solve complex, real-life problems;
Â· understand the principles behind recognized algorithms used in state-of-the-art numerical software;
Â· learn the advantages and limitations of these algorithms, to facilitate the choice of which pre-existing bricks to assemble for solving a given problem; and
Â· acquire methods that allow a critical assessment of numerical results.
Numerical Methods - a Consumer Guide will be of interest to engineers and researchers who solve problems numerically with computers or supervise people doing so, and to students of both engineering and applied mathematics.
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 a radically new approach to problems of evaluating and optimizing the performance of continuous-time stochastic systems. This approach is based on the use of a family of Markov processes called Piecewise-Deterministic Processes (PDPs) as a general class of stochastic system models. A PDP is a Markov process that follows deterministic trajectories between random jumps, the latter occurring either spontaneously, in a Poisson-like fashion, or when the process hits the boundary of its state space. This formulation includes an enormous variety of applied problems in engineering, operations research, management science and economics as special cases; examples include queueing systems, stochastic scheduling, inventory control, resource allocation problems, optimal planning of production or exploitation of renewable or non-renewable resources, insurance analysis, fault detection in process systems, and tracking of maneuvering targets, among many others.
Basic Marketing Research, 8e, International Edition is the best-selling introductory marketing research text because it is accessible to students while maintaining its level of coverage. Basic Marketing Research, International Edition provides a framework for the choices and decisions that must be made by managers - an important aspect of marketing research - because decisions made in one stage of the process have consequences for other stages. Managers and marketing researchers need to appreciate the interactions among the parts of the research process so they can have confidence in a particular research result. This edition provides readers with an overview of the information gathering function from the perspective of the researchers who gather the information and the marketing managers who use it.
As the demand for energy continues to grow, optimization has risen to the forefront of power engineering research and development. Continuing in the bestselling tradition of the first edition, Electric Power System Applications of Optimization, Second Edition presents the theoretical background of optimization from a practical power system point of view, exploring advanced techniques, new directions, and continuous application problems.
The book provides both the analytical formulation of optimization and various algorithmic issues that arise in the application of various methods in power system planning and operation. The second edition adds new functions involving market programs, pricing, reliability, and advances in intelligent systems with implemented algorithms and illustrative examples. It describes recent developments in the field of Adaptive Critics Design and practical applications of approximate dynamic programming. To round out the coverage, the final chapter combines fundamental theories and theorems from functional optimization, optimal control, and dynamic programming to explain new Adaptive Dynamic Programming concepts and variants.
With its one-of-a-kind integration of cornerstone optimization principles with application examples, this second edition propels power engineers to new discoveries in providing optimal supplies of energy.