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This book discusses a new discipline, variational analysis, which contains the calculus of variations, differential calculus, optimization, and variational inequalities. To such classic branches of mathematics, variational analysis provides a uniform theoretical base that represents a powerful tool for the applications. The contributors are among the best experts in the field. Audience The target audience of this book includes scholars in mathematics (especially those in mathematical analysis), mathematical physics and applied mathematics, calculus of variations, optimization and operations research, industrial mathematics, structural engineering, and statistics and economics.
Variational inequalities (Mathematics) --- Mathematical optimization --- Inequalities, Variational (Mathematics) --- Calculus of variations --- Differential inequalities --- Mathematical optimization. --- Global analysis (Mathematics). --- Differential Equations. --- Mathematics. --- Calculus of Variations and Optimal Control; Optimization. --- Analysis. --- Optimization. --- Ordinary Differential Equations. --- Applications of Mathematics. --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- 517.91 Differential equations --- Differential equations --- Calculus of variations. --- Mathematical analysis. --- Analysis (Mathematics). --- Differential equations. --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- 517.1 Mathematical analysis --- Isoperimetrical problems --- Variations, Calculus of --- Mathematics --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal
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The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained.
Nonsmooth optimization --- Variational inequalities (Mathematics) --- Equilibrium --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Balance --- Balance (Physics) --- Balancing (Physics) --- Stability --- Statics --- Inequalities, Variational (Mathematics) --- Calculus of variations --- Differential inequalities --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization
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