Hasil Pencarian  ::  Simpan CSV :: Kembali

"In the past decade, primal-dual algorithms have emerged as the most important and useful algorithms from the interior-point class. This book presents the major primal-dual algorithms for linear programming in straightforward terms. A thorough description of the theoretical properties of these methods is given, as are a discussion of practical and computational aspects and a summary of current software. This is an excellent, timely, and well-written work. The major primal-dual algorithms covered in this book are path-following algorithms (short- and long-step, predictor-corrector), potential-reduction algorithms, and infeasible-interior-point algorithms. A unified treatment of superlinear convergence, finite termination, and detection of infeasible problems is presented. Issues relevant to practical implementation are also discussed, including sparse linear algebra and a complete specification of Mehrotra's predictor-corrector algorithm. Also treated are extensions of primal-dual algorithms to more general problems such as monotone complementarity, semidefinite programming, and general convex programming problems."

"This compact book, through the simplifying perspective it presents, will take a reader who knows little of interior-point methods to within sight of the research frontier, developing key ideas that were over a decade in the making by numerous interior-point method researchers. It aims at developing a thorough understanding of the most general theory for interior-point methods, a class of algorithms for convex optimization problems. The study of these algorithms has dominated the continuous optimization literature for nearly 15 years. In that time, the theory has matured tremendously, but much of the literature is difficult to understand, even for specialists. By focusing only on essential elements of the theory and emphasizing the underlying geometry, A Mathematical View of Interior-Point Methods in Convex Optimization makes the theory accessible to a wide audience, allowing them to quickly develop a fundamental understanding of the material.The author begins with a general presentation of material pertinent to continuous optimization theory, phrased so as to be readily applicable in developing interior-point method theory. This presentation is written in such a way that even motivated Ph.D. students who have never had a course on continuous optimization can gain sufficient intuition to fully understand the deeper theory that follows. Renegar continues by developing the basic interior-point method theory, with emphasis on motivation and intuition. In the final chapter, he focuses on the relations between interior-point methods and duality theory, including a self-contained introduction to classical duality theory for conic programming; an exploration of symmetric cones; and the development of the general theory of primal-dual algorithms for solving conic programming optimization problems.Rather than attempting to be encyclopedic, A Mathematical View of Interior-Point Methods in Convex Optimization gives the reader a solid understanding of the core concepts and relations, the kind of understanding that stays with a reader long after the book is finished."

"Written for specialists working in optimization, mathematical programming, or control theory. The general theory of path-following and potential reduction interior point polynomial time methods, interior point methods, interior point methods for linear and quadratic programming, polynomial time methods for nonlinear convex programming, efficient computation methods for control problems and variational inequalities, and acceleration of path-following methods are covered. In this book, the authors describe the first unified theory of polynomial-time interior-point methods. Their approach provides a simple and elegant framework in which all known polynomial-time interior-point methods can be explained and analyzed; this approach yields polynomial-time interior-point methods for a wide variety of problems beyond the traditional linear and quadratic programs. The book contains new and important results in the general theory of convex programming, e.g., their "conic" problem formulation in which duality theory is completely symmetric. For each algorithm described, the authors carefully derive precise bounds on the computational effort required to solve a given family of problems to a given precision. In several cases they obtain better problem complexity estimates than were previously known. Several of the new algorithms described in this book, e.g., the projective method, have been implemented, tested on "real world" problems, and found to be extremely efficient in practice."

"Regresi kuantil merupakan salah satu teknik regresi dengan memodelkan kuantil dari variabel dependen bersyarat variabel penjelas. Model yang diperoleh dengan regresi kuantil merupakan suatu gambaran lengkap atas perilaku data baik di bagian tengah maupun ekor (tail) sebaran. Sehingga teknik ini baik digunakan untuk analisa data apabila dicurigai adanya perbedaan pengaruh variabel penjelas terhadap bagian-bagian tertentu variabel dependen. Hal ini dapat dilihat dari hasil taksiran parameter regresi kuantil yang berubah secara monoton. Selain itu regresi kuantil juga bagus digunakan pada data dengan nilai ekstrim yang penting untuk dianalisa. Untuk mendapatkan model regresi kuantil diperlukan proses penaksiran parameter yang dilakukan dengan meminimumkan ekspektasi suatu fungsi loss. Proses optimisasi ini selanjutnya diubah ke dalam program linier dan dapat diselesaikan dengan metode interior point. Metode interior point yang digunakan dalam skripsi ini mengacu pada algoritma Frisch-Newton. Selanjutnya pada skripsi ini, regresi kuantil akan diterapkan pada dua data yang masing-masing memiliki karakteristik yang berbeda.

---

Quantile regression is a regression technique by modeling the conditional quantile of the dependent variable. Models obtained with quantile regression is a complete picture of the behavior of the data either in the middle or tail. This technique is well used to analyze data when there is suspected differences in the effect of explanatory variables on the dependent variable. It can be seen from the results of quantile regression parameter estimates which changed monotonically. In addition quantile regression is also good to use on the data with extreme values that are important to be analyzed. To get the required quantile regression model, parameter estimation process is done by minimizing the expectation of a loss function. The optimization process is then converted into a linear program and can be solved by interior point methods. Interior point methods used in this skripsi refers to the Frisch-Newton algorithm. Later in this skripsi, quantile regression will be applied to the two data each has different characteristics."

"This monograph deals with a general class of solution approaches in deterministic global optimization, namely the geometric branch-and-bound methods which are popular algorithms, for instance, in Lipschitzian optimization, d.c. programming, and interval analysis.It also introduces a new concept for the rate of convergence and analyzes several bounding operations reported in the literature, from the theoretical as well as from the empirical point of view. Furthermore, extensions of the prototype algorithm for multicriteria global optimization problems as well as mixed combinatorial optimization problems are considered. Numerical examples based on facility location problems support the theory. Applications of geometric branch-and-bound methods, namely the circle detection problem in image processing, the integrated scheduling and location makespan problem, and the median line location problem in the three-dimensional space are also presented.The book is intended for both researchers and students in the areas of mathematics, operations research, engineering, and computer science."

"This textbook provides a step-by-step approach to numerical methods in engineering modelling. The authors provide a consistent treatment of the topic, from the ground up, to reinforce for students that numerical methods are a set of mathematical modelling tools which allow engineers to represent real-world systems and compute features of these systems with a predictable error rate. Each method presented addresses a specific type of problem, namely root-finding, optimization, integral, derivative, initial value problem, or boundary value problem, and each one encompasses a set of algorithms to solve the problem given some information and to a known error bound. The authors demonstrate that after developing a proper model and understanding of the engineering situation they are working on, engineers can break down a model into a set of specific mathematical problems, and then implement the appropriate numerical methods to solve these problems."

"Dibahan mengenai perencanaan dan penjadwalan jaringan proyek berdasarkan fungsi utilitas. Agar jaringan proyek diselesaikan dalam jangka waktu dan biaya yang minimum, maka utilitas setiap aktifitas pada proyek tersebut harus dimaksimumkan. Model matematis yang mendasarinya adalah pemogramana linear parametrik. Untuk mencari aktifitas yang akan dipercepat jangka waktunya digunakan metode Ford-Fulkerson, sedangkan algoritma Primal-Dual digunakan untuk menetapkan besarnya waktu percepatan."

"In this brief the authors discuss some important subclasses of polynomial optimization models arising from various applications, with a focus on approximations algorithms with guaranteed worst case performance analysis. The brief presents a clear view of the basic ideas underlying the design of such algorithms and the benefits are highlighted by illustrative examples showing the possible applications."