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This book has two main objectives: • to provide a concise introduction to nonlinear optimization methods, which can be used as a textbook at a graduate or upper undergraduate level; • to collect and organize selected important topics on optimization algorithms, not easily found in textbooks, which can provide material for advanced courses or can serve as a reference text for self-study and research. The basic material on unconstrained and constrained optimization is organized into two blocks of chapters: • basic theory and optimality conditions • unconstrained and constrained algorithms. These topics are treated in short chapters that contain the most important results in theory and algorithms, in a way that, in the authors’ experience, is suitable for introductory courses. A third block of chapters addresses methods that are of increasing interest for solving difficult optimization problems. Difficulty can be typically due to the high nonlinearity of the objective function, ill-conditioning of the Hessian matrix, lack of information on first-order derivatives, the need to solve large-scale problems. In the book various key subjects are addressed, including: exact penalty functions and exact augmented Lagrangian functions, non monotone methods, decomposition algorithms, derivative free methods for nonlinear equations and optimization problems. The appendices at the end of the book offer a review of the essential mathematical background, including an introduction to convex analysis that can make part of an introductory course.

Mathematical optimization. --- Mathematical optimization --- Nonlinear theories --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Methodology. --- Operations research. --- Computer science—Mathematics. --- Engineering mathematics. --- Engineering—Data processing. --- Continuous Optimization. --- Operations Research and Decision Theory. --- Mathematics of Computing. --- Mathematical and Computational Engineering Applications. --- Engineering --- Engineering analysis --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Mathematics --- Optimització matemàtica --- Teories no lineals

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Vengono descritti e analizzati gli algoritmi più significativi per la soluzione di problemi di ottimizzazione non vincolata e di sistemi di equazioni non lineari. Particolare attenzione è rivolta allo studio della convergenza globale e delle tecniche di globalizzazione che costituiscono uno dei maggiori contributi dell' ottimizzazione al calcolo numerico. Nel volume vengono considerati sia gli algoritmi più noti che quelli proposti recentemente nella letteratura specialistica e che non sono usualmente inclusi nei libri a carattere introduttivo sui metodi di ottimizzazione. La stesura del testo è tale da renderlo adatto sia a un lettore che intenda acquisire una preparazione di base sui metodi di ottimizzazione non vincolata, sia a un lettore che abbia già competenze generali sulle tecniche di ottimizzazione e voglia approfondire specifici argomenti. Il libro è corredato da varie appendici finalizzate a rendere la trattazione il più possibile autocontenuta.

Industrial economics --- Engineering sciences. Technology --- Computer. Automation --- automatisering --- informatica --- wiskunde --- industriële marketing --- ingenieurswetenschappen

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This volume collects peer-reviewed short papers presented at the Optimization and Decision Science conference (ODS 2022) held in Florence (Italy) from August 30th to September 2nd, 2022, organized by the Global Optimization Laboratory within the University of Florence and AIRO (the Italian Association for Operations Research). The book includes contributions in the fields of operations research, optimization, problem solving, decision making and their applications in the most diverse domains. Moreover, a special focus is set on the challenging theme Operations Research: inclusion and equity. The work offers 30 contributions, covering a wide spectrum of methodologies and applications. Specifically, they feature the following topics: (i) Variational Inequalities, Equilibria and Games, (ii) Optimization and Machine Learning, (iii) Global Optimization, (iv) Optimization under Uncertainty, (v) Combinatorial Optimization, (vi) Transportation and Mobility, (vii) Health Care Management, and (viii) Applications. This book is primarily addressed to researchers and PhD students of the operations research community. However, due to its interdisciplinary content, it will be of high interest for other closely related research communities.

Operational research. Game theory --- Mathematical statistics --- Planning (firm) --- Business management --- management --- mathematische modellen --- econometrie --- operationeel onderzoek