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Linear programming. --- Convex programming.

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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.

Interior-point methods. --- Mathematical optimization. --- Convex programming.

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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.

Convex programming --- Mathematical optimization --- Convex programming. --- Mathematical optimization. --- Optimisation mathématique --- Programmation linéaire --- Programmation convexe

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Mathematical optimization --- Convex programming --- Duality theory (Mathematics) --- Congresses --- Congresses. --- Mathematical control systems --- Planning (firm) --- Operational research. Game theory --- Mathematical optimization - Congresses --- Convex programming - Congresses --- Duality theory (Mathematics) - Congresses

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Planning (firm) --- 519.7 --- Convex programming --- Programming (Mathematics) --- Mathematical cybernetics --- 519.7 Mathematical cybernetics --- Théorie des jeux --- Programmation mathematique --- Analyse convexe --- Programmation convexe