Mathematical optimization

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  • mathematical optimization least-squares and linear programming convex optimization example course goals and topics nonlinear optimization brief history of convex optimization

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  • The favorable reception of Portfolio Management Formulas exceeded even the greatest expectation I ever had for the book. I had written it to promote the concept of optimal f and begin to immerse readers in portfolio theory and its missing relationship with optimal f. Besides finding friends out there, Portfolio Management Formulas was surprisingly met by quite an appetite for the math concerning money management. Hence this book. I am indebted to Karl Weber, Wendy Grau, and others at John Wiley & Sons who allowed me the necessary latitude this book required....

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  • Robotics and computer vision are interdisciplinary subjects at the intersection of engineering and computer science. By their nature, they deal with both computers and the physical world. Although the former are in the latter, the workings of computers are best described in the black-and-white vocabulary of discrete mathematics, which is foreign to most classical models of reality, quantum physics notwithstanding. This class surveys some of the key tools of applied math to be used at the interface of continuous and discrete. It is not on robotics or computer vision.

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  • Stochastic Calculus of Variations (or Malliavin Calculus) consists, in brief, in constructing and exploiting natural differentiable structures on abstract probability spaces; in other words, Stochastic Calculus of Variations proceeds from a merging of differential calculus and probability theory. As optimization under a random environment is at the heart of mathematical finance, and as differential calculus is of paramount importance for the search of extrema, it is not surprising that Stochastic Calculus of Variations appears in mathematical finance.

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  • This is the first volume of the Paris-Princeton Lectures in Financial Mathematics. The goal of this series is to publish cutting edge research in self-contained articles prepared by well known leaders in the field, or promising young researchers invited by the editors to contribute to a volume. Particular attention is paid to the quality of the exposition and we aim at articles that can serve as an introductory reference for research in the field. The series is a result of frequent exchanges between researchers in finance and financial mathematics in Paris and Princeton.

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  • This book introduces a variety of problem statements in classical optimal control, in optimal estimation and filtering, and in optimal control problems with non-scalar-valued performance criteria. Many example problems are solved completely in the body of the text. All chapter-end exercises are sketched in the appendix. The theoretical part of the book is based on the calculus of variations, so the exposition is very transparent and requires little mathematical rigor.

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  • As you will see, the maths shows that the trick will always work if the spectator does what’s expected of them and follows the rules. Mathematically we call the things the spectator must do, like choose different digits and put them in the right order, the constraints. In this trick it’s the presentation (where we say ‘lets make it harder’ and so on) that makes sure these constraints are followed. If we let things go astray and, for example, let the spectator choose digits that were the same we would have a constraint violation and it would upset the maths....

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  • Continuing interest in the subject of reliability and the heretofore unavailability of our book Mathematical Theory of Reliability have encouraged publication of this SIAM Classics edition. We have not revised the original version, although much has transpired since its original publication in 1965. Although many contemporary reliability books are now available, few provide as mathematically rigorous a treatment of the required probability background as this one.

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  • Mathematical modelling is the process of formulating an abstract model in terms of mathematical language to describe the complex behaviour of a real system. Mathematical models are quantitative models and often expressed in terms of ordinary differential equations and partial differential equations. Mathematical models can also be statistical models, fuzzy logic models and empirical relationships. In fact, any model description using mathematical language can be called a mathematical model.

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  • Ant Colony Optimization (ACO) is the best example of how studies aimed at understanding and modeling the behavior of ants and other social insects can provide inspiration for the development of computational algorithms for the solution of difficult mathematical problems. Introduced by Marco Dorigo in his PhD thesis (1992) and initially applied to the travelling salesman problem, the ACO field has experienced a tremendous growth, standing today as an important nature-inspired stochastic metaheuristic for hard optimization problems....

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  • Mathematical Modeling I – preliminary is designed for undergraduate students. Two other followup books, Mathematical Modeling II – advanced and Mathematical Modeling III – case studies in biology, will be published. II and III will be designed for both graduate students and undergraduate students. All the three books are independent and useful for study and application of mathematical modeling in any discipline.

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  • Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài:Asymptotically optimal pairing strategy for Tic-Tac-Toe with numerous directions...

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  • Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Optimal Packings of 13 and 46 Unit Squares in a Square...

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  • Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: On optimal linear codes over F8...

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  • Optimization has become pervasive in medicine. The application of computing to medical applications has opened many challenging issues and problems for both the medical computing field and the mathematical community. Mathematical techniques (continuous and discrete) are playing a key role with increasing importance in understanding several fundamental problems in medicine. Naturally, optimization is a fundamentally important tool due to the limitation of the resources involved and the need for better decision making....

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  • Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: An optimal strongly identifying code in the infinite triangular grid...

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  • The research of optimal condition for etching silicon in TMAH solution with controlled etch rate and low surface roughness is the purpose of this study. The investigation on the influence of temperature, agitation, size of etch-window, etch time on etch rate and the surface roughness were carried out. With the TMAH concentration of 20% in weight, the optimal etching conditions were as follows: temperature of about 80 – 90 oC, agitation of 150 - 200 rpm. The etch rate is controlled in range of 0.49 – 0.72 µm/min. ...

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  • Lecture Mathematics 53 - Lecture 3.3 presents the absolute extrema and optimization. The main contents of this chapter include all of the following: Definitions and examples, absolute extrema of functions on closed and bounded intervals, absolute extrema of functions with one relative extremum, other cases: using limits.

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  • In this concept, you will learn to find the optimal value of a function that is associated with an optimization problem. At this point, you know how to analyze a function to find its minima and maxima using the first and second derivatives. This is a big deal! Finding the solution to some real-world problem (such as in finance, science, and engineering) often involves a process of finding the maximum or minimum of a function within an acceptable region of values.

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  • I have been undertaking the research and practical applications of power system optimization since the early 1980s. In the early stage of my career, I worked in universities such as Chongqing University (China), Brunel University (UK), National University of Singapore, and Howard University (USA). Since 2000 I have been working for AREVA T & D Inc (USA). When I was a full - time professor at Chongqing University, I wrote a tutorial on power system optimal operation, which I used to teach my senior undergraduate students and postgraduate students in power engineering until 1996.

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