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Book
Convex functions
Authors: ---
ISBN: 9780521850056 0521850053 9781139087322 9781139811798 1139811797 9781139637282 1139637282 1139087320 9781139811545 1139811541 1139106619 1139811347 1283870851 1139811673 1139811428 Year: 2010 Volume: 109 Publisher: Cambridge Cambridge University Press

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Abstract

Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. This book, which is the product of a collaboration of over 15 years, is unique in that it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics and applications, treating convex functions in both Euclidean and Banach spaces. The book can either be read sequentially for a graduate course, or dipped into by researchers and practitioners. Each chapter contains a variety of specific examples, and over 600 exercises are included, ranging in difficulty from early graduate to research level.


Book
Convex optimization in signal processing and communications
Authors: ---
ISBN: 9780521762229 0521762227 9780511804458 9780511691232 0511691238 9780511692352 0511692358 0511804458 1107208122 9781107208124 1282653261 9781282653269 9786612653261 6612653264 0511689756 9780511689758 0511690495 9780511690495 0511689004 9780511689000 Year: 2010 Publisher: Cambridge New York Cambridge University Press

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Over the past two decades there have been significant advances in the field of optimization. In particular, convex optimization has emerged as a powerful signal processing tool, and the variety of applications continues to grow rapidly. This book, written by a team of leading experts, sets out the theoretical underpinnings of the subject and provides tutorials on a wide range of convex optimization applications. Emphasis throughout is on cutting-edge research and on formulating problems in convex form, making this an ideal textbook for advanced graduate courses and a useful self-study guide. Topics covered range from automatic code generation, graphical models, and gradient-based algorithms for signal recovery, to semidefinite programming (SDP) relaxation and radar waveform design via SDP. It also includes blind source separation for image processing, robust broadband beamforming, distributed multi-agent optimization for networked systems, cognitive radio systems via game theory, and the variational inequality approach for Nash equilibrium solutions.


Book
Conjugate duality in convex optimization
Author:
ISBN: 3642048994 9786612834943 3642049001 1282834940 Year: 2010 Publisher: Berlin ; London : Springer,

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This book presents new achievements and results in the theory of conjugate duality for convex optimization problems. The perturbation approach for attaching a dual problem to a primal one makes the object of a preliminary chapter, where also an overview of the classical generalized interior point regularity conditions is given. A central role in the book is played by the formulation of generalized Moreau-Rockafellar formulae and closedness-type conditions, the latter constituting a new class of regularity conditions, in many situations with a wider applicability than the generalized interior point ones. The reader also receives deep insights into biconjugate calculus for convex functions, the relations between different existing strong duality notions, but also into several unconventional Fenchel duality topics. The final part of the book is consecrated to the applications of the convex duality theory in the field of monotone operators.

Keywords

Convex functions. --- Duality theory (Mathematics). --- Mathematical optimization. --- Convex functions --- Duality theory (Mathematics) --- Mathematical optimization --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Monotone operators. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Functions, Convex --- Mathematics. --- Operations research. --- Decision making. --- Mathematical analysis. --- Analysis (Mathematics). --- System theory. --- Management science. --- Operations Research, Management Science. --- Operation Research/Decision Theory. --- Optimization. --- Systems Theory, Control. --- Analysis. --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Operator theory --- Algebra --- Topology --- Functions of real variables --- Systems theory. --- Global analysis (Mathematics). --- Operations Research/Decision Theory. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- 517.1 Mathematical analysis --- Systems, Theory of --- Systems science --- Science --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Quantitative business analysis --- Statistical decision --- Philosophy --- Decision making


Book
IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials : proceedings of the IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, Bochum, Germany, September 22-26, 2008
Authors: --- ---
ISBN: 9048191947 9786613002686 128300268X 9048191955 Year: 2010 Publisher: Dordrecht : Springer,

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Abstract

The symposium focused on novel applications of methods from the calculus of variations to the solid mechanics of materials, including the development of new material models as well as the advancement of the corresponding computational techniques. Specific emphasis was put on the treatment of materials posessing an inherent microstructure and thus exhibiting a behavior which fundamentally involves multiple scales. Among the topic treated in this volume are: Energy-based modeling of material microstructures; modeling of the evolution of material microstructures; micromechanical modeling of shape-memory alloys; variational multiscale methods and associated numerical procedures; and micromechanics of multifield and multiphysics problems.

Keywords

Materials -- Mechanical properties -- Congresses. --- Materials --- Engineering & Applied Sciences --- Chemical & Materials Engineering --- Applied Mathematics --- Materials Science --- Mechanical properties --- Calculus of variations. --- Control theory. --- Mathematical optimization. --- Convex functions. --- Functions, Convex --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Isoperimetrical problems --- Variations, Calculus of --- Engineering. --- Mathematical analysis. --- Analysis (Mathematics). --- Mathematical models. --- Applied mathematics. --- Engineering mathematics. --- Continuum mechanics. --- Continuum Mechanics and Mechanics of Materials. --- Calculus of Variations and Optimal Control; Optimization. --- Mathematical Modeling and Industrial Mathematics. --- Analysis. --- Appl.Mathematics/Computational Methods of Engineering. --- Maxima and minima --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Engineering --- Engineering analysis --- Mathematical analysis --- Models, Mathematical --- Simulation methods --- 517.1 Mathematical analysis --- Construction --- Industrial arts --- Technology --- Mathematics --- Functions of real variables --- Operations research --- System analysis --- Dynamics --- Machine theory --- Mechanics. --- Mechanics, Applied. --- Global analysis (Mathematics). --- Solid Mechanics. --- Mathematical and Computational Engineering. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Quantum theory --- Solids. --- Calculus of Variations and Optimization. --- Mathematical and Computational Engineering Applications. --- Data processing. --- Solid state physics --- Transparent solids

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