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Mathematics --- Mathematics. --- Wiskunde. --- Math --- algebra --- mathematical physics --- probability theory --- statistics --- differential equations --- functional analysis --- approximation theory --- iteration methods --- fixed point theory --- nonsmooth analysis --- variational analysis --- Science

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This book contains refereed papers which were presented at the 34th Workshop of the International School of Mathematics "G. Stampacchia,” the International Workshop on Optimization and Control with Applications. The book contains 28 papers that are grouped according to four broad topics: duality and optimality conditions, optimization algorithms, optimal control, and variational inequality and equilibrium problems. The specific topics covered in the individual chapters include optimal control, unconstrained and constrained optimization, complementarity and variational inequalities, equilibrium problems, semi-definite programs, semi-infinite programs, matrix functions and equations, nonsmooth optimization, generalized convexity and generalized monotinicity, and their applications. Audience This book is suitable for researchers, practitioners, and postgraduate students in optimization, operations research, and optimal control.

Mathematical optimization. --- Control theory. --- Nonsmooth optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Dynamics --- Machine theory --- Optimization.

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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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This volume looks at the study of dynamical systems with discontinuities. Discontinuities arise when systems are subject to switches, decisions, or other abrupt changes in their underlying properties that require a ‘non-smooth’ definition. A review of current ideas and introduction to key methods is given, with a view to opening discussion of a major open problem in our fundamental understanding of what nonsmooth models are. What does a nonsmooth model represent: an approximation, a toy model, a sophisticated qualitative capturing of empirical law, or a mere abstraction? Tackling this question means confronting rarely discussed indeterminacies and ambiguities in how we define, simulate, and solve nonsmooth models. The author illustrates these with simple examples based on genetic regulation and investment games, and proposes precise mathematical tools to tackle them. The volume is aimed at students and researchers who have some experience of dynamical systems, whether as a modelling tool or studying theoretically. Pointing to a range of theoretical and applied literature, the author introduces the key ideas needed to tackle nonsmooth models, but also shows the gaps in understanding that all researchers should be bearing in mind. Mike Jeffrey is a researcher and lecturer at the University of Bristol with a background in mathematical physics, specializing in dynamics, singularities, and asymptotics.

Dynamics. --- Ergodic theory. --- Mathematical models. --- Dynamical Systems and Ergodic Theory. --- Mathematical Modeling and Industrial Mathematics. --- Nonsmooth optimization. --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Models, Mathematical --- Simulation methods --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics

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This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as is multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. The main purpose of this book is to provide a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method. This method is an effective and flexible technique to obtain existence and comparison results of solutions. Also, it can be employed for the investigation of various qualitative properties, such as location, multiplicity and extremality of solutions. In the treatment of the problems under consideration a wide range of methods and techniques from nonlinear and nonsmooth analysis is applied, a brief outline of which has been provided in a preliminary chapter in order to make the book self-contained. This text is an invaluable reference for researchers and graduate students in mathematics (functional analysis, partial differential equations, elasticity, applications in materials science and mechanics) as well as physicists and engineers.

Variational inequalities (Mathematics) --- Nonsmooth optimization. --- Functional analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Inequalities, Variational (Mathematics) --- Differential inequalities --- Differential equations, partial. --- Mathematics. --- Functional Analysis. --- Partial Differential Equations. --- Applications of Mathematics. --- Math --- Science --- Partial differential equations --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics --- Differential equations. --- Differential Equations. --- 517.91 Differential equations --- Differential equations