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Convex programming --- Linear programming --- Relaxation methods (Mathematics)

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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

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517.51 --- Functions of a real variable. Real functions --- Convex functions. --- Convex sets. --- Convex programming. --- 517.51 Functions of a real variable. Real functions --- Convex functions --- Convex programming --- Convex sets --- Sets, Convex --- Convex domains --- Set theory --- Programming (Mathematics) --- Functions, Convex --- Functions of real variables --- Convex geometry. --- Géométrie convexe. --- Fonctions convexes. --- Géometrie convexe --- Analyse convexe --- Programmation mathematique --- Programmation convexe

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An updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces, 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. Finally, the structure of the book has been modified to highlight the most recent progression in the field including fundamental results on the theory of infinite-dimensional convex analysis and includes helpful bibliographical notes at the end of each chapter.

Banach spaces. --- Convex functions. --- Hilbert space. --- Mathematical optimization. --- Banach spaces --- Hilbert space --- Convex functions --- Convex programming --- Mathematics --- Civil & Environmental Engineering --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Operations Research --- Calculus --- Convex programming. --- Functions, Convex --- Mathematics. --- Optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Math --- Science --- Programming (Mathematics) --- Functions of real variables --- Hyperspace --- Inner product spaces --- Functions of complex variables --- Generalized spaces --- Topology

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Optimization is ubiquitous in power system engineering. Drawing on powerful, modern tools from convex optimization, this rigorous exposition introduces essential techniques for formulating linear, second-order cone, and semidefinite programming approximations to the canonical optimal power flow problem, which lies at the heart of many different power system optimizations. Convex models in each optimization class are then developed in parallel for a variety of practical applications like unit commitment, generation and transmission planning, and nodal pricing. Presenting classical approximations and modern convex relaxations side-by-side, and a selection of problems and worked examples, this is an invaluable resource for students and researchers from industry and academia in power systems, optimization, and control.

Electric power systems --- Electric power distribution --- Convex programming --- Mathematical optimization --- Mathematical models --- Mathematics --- 621.315 --- Convex programming. --- Mathematical optimization. --- Programming (Mathematics) --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Electricity --- Power distribution, Electric --- Power transmission --- Electric power transmission --- Electrification --- Transmission of electric energy. Power distribution and telecommunication lines. Conductors. Insulating materials. Accessories. Design, construction of lines --- Mathematics. --- Distribution --- 621.315 Transmission of electric energy. Power distribution and telecommunication lines. Conductors. Insulating materials. Accessories. Design, construction of lines --- Electric power systems - Mathematical models --- Electric power distribution - Mathematics