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.
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.
Enhancing Practice through Classroom Research addresses the growing trend in educational contexts for teachers to engage in CPD and develop as excellent practitioners. It#xE3;#xAC;#xAC;is a guide for teachers, by teachers, on how to improve practice - and understanding of practice - through a personal process of reflection, research and action. The book will provide much needed guidance for teachers engaged in postgraduate studies in reflective practice and professional development, and structured around real life examples of research undertaken by teachers, it will be highly supportive for teachers in the classroom interested in small-scale research projects. The book presents a framework beginning and developing research, in four key sections: Section one deals with reflection on practice, exploring concerns about practice and identifying values; section two examines ideas around why practitioners might be concerned about their practice; section three outlines how readers can develop a personal action plan and gather data to show any changes or possible improvements in their work; the final section shows how readers can draw on the evidence they have produced to develop their own personal theory of education. It covers key issues central to effective professional development and improving practice in the classroom: Understanding the concept of the professional and reflecting on how values inform practice Identifying critical questions such as why you teach as you do Deciding how to investigate the issues you#xE2;#xAC;"ve identified #xE2;#xAC;#x1C; developing a research plan and collecting data Interpreting and making meaning from data Writing up each stage of your research Each section includes two chapters, the first describing real life experiences of researching and reflection in the classroom, giving the reader the opportunity to use the studies to think critically and reflect on their own practice. The second chapter explains a specific stage of the research process project and its rationale, and includes tasks throughout for readers to undertake to encourage reflection.
This is a simple guide to search engine optimization, written in layman's simplicity, geared specifically toward authors and using the best genre keywords for writers to use on blogs and book distributors such as Amazon. It is basic, basic, basic. No mention of HTML or any kind of coding. In fact, if you dabble in website coding or have any previous knowledge of how basic SEO works, keep on scrolling to other optimization guides. I know, I know. Book descriptions are supposed to encourage buying of this particular book. And you should if you are brand spanking new to how search engines and web crawlers work. But if you're looking for more advanced coding, this isn't the guide for that. Not by a long shot. So writers and bloggers new to search engine optimization, this short (25 pages) guide with screen shot examples is ideal. More advanced SEO specialists...move along. From Author Lavender Daye: "Most of the writers who buy this will be like me: desperately in need of the information and how to incorporate it, but with little (or slowly developing) techno savvy."