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"Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization. The study of this theory is expanding with the development of efficient algorithms and applications to a number of diverse disciplines like matrix theory, operations research, and economics. This self-contained book is designed to provide a novel insight into optimization on discrete structures and should reveal unexpected links among different disciplines. It is the first and only English-language monograph on the theory and applications of discrete convex analysis."

"Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications presents and analyzes numerous engineering models, illustrating the wide spectrum of potential applications of the new theoretical and algorithmical techniques emerging from the significant progress taking place in convex optimization. It is hoped that the information provided here will serve to promote the use of these techniques in engineering practice. The book develops a kind of "algorithmic calculus" of convex problems, which can be posed as conic quadratic and semidefinite programs. This calculus can be viewed as a "computationally tractable" version of the standard convex analysis."

"This book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and application. This edition has been updated to include new results pertaining to advanced concepts of subdifferential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research concerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems. "

"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."

"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."

"A study of how complexity questions in computing interact with classical mathematics in the numerical analysis of issues in algorithm design. Algorithmic designers concerned with linear and nonlinear combinatorial optimization will find this volume especially useful. Two algorithms are studied in detail: the ellipsoid method and the simultaneous diophantine approximation method. Although both were developed to study, on a theoretical level, the feasibility of computing some specialized problems in polynomial time, they appear to have practical applications. The book first describes use of the simultaneous diophantine method to develop sophisticated rounding procedures. Then a model is described to compute upper and lower bounds on various measures of convex bodies. Use of the two algorithms is brought together by the author in a study of polyhedra with rational vertices. The book closes with some applications of the results to combinatorial optimization."

"Jadwal pengiriman memainkan peranan penting dalam setiap rantai pasokan minyak bumi, karena faktor ini memiliki pengaruh yang cukup besar dalam pembiayaan. Oleh karena itu, dibutuhkan suatu sistem penjadwalan yang meminimalkan biaya transportasi. Dalam skripsi ini, akan dipelajari model optimasi taktis untuk distribusi minyak mentah oleh 2 jenis kapal tanker. Adapun masalah yang akan dibahas adalah penjadwalan pengiriman melalui rute yang menghubungkan platform (tempat produksi minyak mentah) dan terminal (tempat pengolahan minyak mentah), dengan tujuan untuk mengirimkan produk dari platform ke terminal dengan biaya transportasi minimum dalam perencanaan waktu tertentu. Untuk setiap tempat, tingkat persediaan harus terletak antara batas bawah dan batas atas. Hal tersebut untuk menghindari kekurangan ataupun kelebihan produk. Pada setiap tempat, pengiriman diproses untuk keseluruhan perencanaan yang telah ditentukan. Proses penjadwalan akan dilakukan berdasarkan hasil perhitungan convex hull dari knapsack dua variabel dengan menggunakan metode branch and bound untuk memecahkan masalah knapsack. Kesimpulan yang diperoleh adalah bahwa masalah penjadwalan tanker dapat dimodelkan dalam bentuk permasalahan knapsack, dengan hasil berupa jadwal pengiriman tanker beserta asal dan tujuannya.

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Shipment schedule plays a fundamental role in every petroleum supply chain, because this factor has a considerable influence in financing. Hence, it takes a schedule that minimizes transportation cost. In this paper, we study a tactical optimization model for crude oil distribution by 2 types of tankers. The problem consists of scheduling the shipments through routes linking platforms (crude oil production sites) and terminals (crude oil processing sites). The objective is to ship the products from the platforms to supply the terminals with minimum transportation cost for a finite planning horizon. For each site, the inventory levels must lie between a lower and an upper bound to avoid the lack or excess of product. At each site, shipments are processed for the whole planning horizon. Scheduling process will be carried out based on the result of convex hulls calculation of a knapsack two variables with using the branch and bound method to solve the knapsack problem The conclusion is that the tanker scheduling problem can be modeled in the form of knapsack problem, with the results in the form of shipments schedule with source and destination of a tankers."

"Efisiensi penggunaan sumber daya spektrum frekuensi yang terbatas merupakan target utama dari sistem komunikasi nirkabel. Keterbatasan spektrum frekuensi ini, telah mendorong para peneliti untuk mengembangkan komunikasi nirkabel full-duplex. Pada penelitian ini penulis mengusulkan skema optimasi penggunaan daya pada kanal MIMO full-duplex yang telah dilengkapi dengan teknik selfinterference cancellation pada domain propagasi.Pada penelitian ini diturunkan dan dianalisis persamaan mencari daya optimum dari sebuah kanal MIMO fullduplex yang akan menghasilkan kapasitas maksimum dengan menggunakan metode optimasi konveks. Berdasarkan hasil perhitungan terhadap kanal yang telah dioptimasi dapat dibuktikan bahwa kapasitas kanal meningkat sebesar 9 % pada penggunaan daya total sebesar 4 dB dan N=4 dibandingkan kapasitas kanal tanpa optimasi.

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Improving spectral efficiency driven by the limited frequency resources is a key target of the wireless communication system. The limitation of the frequency spectrum has led researchers to develop a full-duplex wireless communication. In this research, author proposes a power optimization scheme of full-duplex MIMO channel that has been equipped with self-interference cancellation techniques in the propagation domain.

In this research, by using convex optimization method, the expression of the optimum power scheme to achieve the maximum capacity of full-duplex MIMO channel is derived and analyzed. Calculation result shows that the capacity of the optimized channel increase 9 % at the total power 4 dB and N=4 compare with channel without optimization."