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Peter B. Morgan's Explanation of Constrained Optimization for Economists is an accessible, user-friendly guide that provides explanations, both written and visual, of the manner in which many constrained optimization problems can be solved.

Constrained optimization. --- Economics, Mathematical. --- Economics --- Mathematical economics --- Econometrics --- Mathematics --- Optimization, Constrained --- Mathematical optimization --- Methodology --- Constrained optimization --- Economics, Mathematical --- E-books

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In dieser Arbeit werden zur Überwachung von Drei-Wege-Katalysatoren zwei neue modellbasierte On-Board-Diagnoseverfahren vorgestellt. Zunächst wurde ein die Alterung mit berücksichtigendes physikalisches Katalysatormodell entwickelt. Dieses bildet die Grundlage der neuen Diagnoseverfahren, bei denen ein den aktuellen Zustand des Katalysators schätzender Sigma-Punkt-Kalman-Filter zum Einsatz kommt. Das große Potential dieser neuen Diagnoseverfahren zeigen die abschließend präsentierten Ergebnisse.

Abgastemperatur --- Spektrale Verfahren --- Constrained Sigma-Punkt-Kalman-Filter --- Drei-Wege-Katalysator-Modell --- On-Board-Diagnose

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Two approaches are known for solving large-scale unconstrained optimization problems—the limited-memory quasi-Newton method (truncated Newton method) and the conjugate gradient method. This is the first book to detail conjugate gradient methods, showing their properties and convergence characteristics as well as their performance in solving large-scale unconstrained optimization problems and applications. Comparisons to the limited-memory and truncated Newton methods are also discussed. Topics studied in detail include: linear conjugate gradient methods, standard conjugate gradient methods, acceleration of conjugate gradient methods, hybrid, modifications of the standard scheme, memoryless BFGS preconditioned, and three-term. Other conjugate gradient methods with clustering the eigenvalues or with the minimization of the condition number of the iteration matrix, are also treated. For each method, the convergence analysis, the computational performances and the comparisons versus other conjugate gradient methods are given. The theory behind the conjugate gradient algorithms presented as a methodology is developed with a clear, rigorous, and friendly exposition; the reader will gain an understanding of their properties and their convergence and will learn to develop and prove the convergence of his/her own methods. Numerous numerical studies are supplied with comparisons and comments on the behavior of conjugate gradient algorithms for solving a collection of 800 unconstrained optimization problems of different structures and complexities with the number of variables in the range [1000,10000]. The book is addressed to all those interested in developing and using new advanced techniques for solving unconstrained optimization complex problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master students in mathematical programming, will find plenty of information and practical applications for solving large-scale unconstrained optimization problems and applications by conjugate gradient methods.

Conjugate gradient methods. --- Constrained optimization. --- Optimization, Constrained --- Mathematical optimization --- Gradient methods, Conjugate --- Approximation theory --- Equations --- Iterative methods (Mathematics) --- Numerical solutions --- Mathematical optimization. --- Mathematical models. --- Optimization. --- Mathematical Modeling and Industrial Mathematics. --- Models, Mathematical --- Simulation methods --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- System analysis

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This book introduces, in an accessible way, the basic elements of Numerical PDE-Constrained Optimization, from the derivation of optimality conditions to the design of solution algorithms. Numerical optimization methods in function-spaces and their application to PDE-constrained problems are carefully presented. The developed results are illustrated with several examples, including linear and nonlinear ones. In addition, MATLAB codes, for representative problems, are included. Furthermore, recent results in the emerging field of nonsmooth numerical PDE constrained optimization are also covered. The book provides an overview on the derivation of optimality conditions and on some solution algorithms for problems involving bound constraints, state-constraints, sparse cost functionals and variational inequality constraints.

Mathematics. --- Optimization. --- Partial Differential Equations. --- Numerical Analysis. --- Differential equations, partial. --- Numerical analysis. --- Mathematical optimization. --- Mathématiques --- Analyse numérique --- Optimisation mathématique --- Mathematical models. --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- 519.63 --- Numerical methods for solution of partial differential equations --- 519.63 Numerical methods for solution of partial differential equations --- Differential equations, Partial. --- Constrained optimization. --- Optimization, Constrained --- Partial differential equations --- Partial differential equations. --- Mathematical optimization --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis

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This book makes available a self-contained collection of modern research addressing the general constrained optimization problems using evolutionary algorithms. Broadly the topics covered include constraint handling for single and multi-objective optimizations; penalty function based methodology; multi-objective based methodology; new constraint handling mechanism; hybrid methodology; scaling issues in constrained optimization; design of scalable test problems; parameter adaptation in constrained optimization; handling of integer, discrete and mix variables in addition to continuous variables; application of constraint handling techniques to real-world problems; and constrained optimization in dynamic environment. There is also a separate chapter on hybrid optimization, which is gaining lots of popularity nowadays due to its capability of bridging the gap between evolutionary and classical optimization. The material in the book is useful to researchers, novice, and experts alike. The book will also be useful for classroom teaching and future research.

Engineering. --- Computational Intelligence. --- Artificial Intelligence (incl. Robotics). --- Mechanical Engineering. --- Optimization. --- Artificial intelligence. --- Mathematical optimization. --- Mechanical engineering. --- Ingénierie --- Intelligence artificielle --- Optimisation mathématique --- Génie mécanique --- Engineering & Applied Sciences --- Computer Science --- Constrained optimization. --- Optimization, Constrained --- Computational intelligence. --- Engineering, Mechanical --- Engineering --- Machinery --- Steam engineering --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Fifth generation computers --- Neural computers --- Construction --- Industrial arts --- Technology --- Mathematical optimization --- Artificial Intelligence.