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Convex functions --- Monotonic functions --- Geometry --- Operational research. Game theory --- Mathematical optimization. --- Operations research. --- Decision making. --- Calculus of variations. --- Optimization. --- Operations Research/Decision Theory. --- Calculus of Variations and Optimal Control; Optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis --- Decision making

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Riemannian, symplectic and complex geometry are often studied by means ofsolutions to systems ofnonlinear differential equations, such as the equa­ tions of geodesics, minimal surfaces, pseudoholomorphic curves and Yang­ Mills connections. For studying such equations, a new unified technology has been developed, involving analysis on infinite-dimensional manifolds. A striking applications of the new technology is Donaldson's theory of "anti-self-dual" connections on SU(2)-bundles over four-manifolds, which applies the Yang-Mills equations from mathematical physics to shed light on the relationship between the classification of topological and smooth four-manifolds. This reverses the expected direction of application from topology to differential equations to mathematical physics. Even though the Yang-Mills equations are only mildly nonlinear, a prodigious amount of nonlinear analysis is necessary to fully understand the properties of the space of solutions. . At our present state of knowledge, understanding smooth structures on topological four-manifolds seems to require nonlinear as opposed to linear PDE's. It is therefore quite surprising that there is a set of PDE's which are even less nonlinear than the Yang-Mills equation, but can yield many of the most important results from Donaldson's theory. These are the Seiberg-Witte~ equations. These lecture notes stem from a graduate course given at the University of California in Santa Barbara during the spring quarter of 1995. The objective was to make the Seiberg-Witten approach to Donaldson theory accessible to second-year graduate students who had already taken basic courses in differential geometry and algebraic topology.

Global analysis (Mathematics) --- Four-manifolds (Topology) --- Mathematical Theory --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Analyse globale (Mathematiques) --- Globale analyse (Wiskunde) --- Trois-variétés (Topologie) --- Vier-menigvuldigheden (Topologie) --- Analyse globale (Mathématiques) --- Variétés topologiques à 4 dimensions --- Algebra. --- Algebraic topology. --- Calculus of variations. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- System theory. --- Algebraic geometry. --- Algebraic Topology. --- Calculus of Variations and Optimal Control; Optimization. --- Global Analysis and Analysis on Manifolds. --- Systems Theory, Control. --- Algebraic Geometry. --- Algebraic geometry --- Systems, Theory of --- Systems science --- Science --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Mathematical analysis --- Philosophy

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The primary aim of this book is to present notions of convex analysis which constitute the basic underlying structure of argumentation in economic theory and which are common to optimization problems encountered in many applications. The intended readers are graduate students, and specialists of mathematical programming whose research fields are applied mathematics and economics. The text consists of a systematic development in eight chapters, with guided exercises containing sometimes significant and useful additional results. The book is appropriate as a class text, or for self-study.

Operational research. Game theory --- Convex functions --- Mathematical optimization --- Applied mathematics. --- Engineering mathematics. --- Economic theory. --- Operations research. --- Decision making. --- Calculus of variations. --- Applications of Mathematics. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Operations Research/Decision Theory. --- Calculus of Variations and Optimal Control; Optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Economic theory --- Political economy --- Social sciences --- Economic man --- Engineering --- Engineering analysis --- Mathematical analysis --- Decision making --- Mathematics

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Constraint Programming is a problem-solving paradigm that establishes a clear distinction between two pivotal aspects of a problem: (1) a precise definition of the constraints that define the problem to be solved and (2) the algorithms and heuristics enabling the selection of decisions to solve the problem. It is because of these capabilities that Constraint Programming is increasingly being employed as a problem-solving tool to solve scheduling problems. Hence the development of Constraint-Based Scheduling as a field of study. The aim of this book is to provide an overview of the most widely used Constraint-Based Scheduling techniques. Following the principles of Constraint Programming, the book consists of three distinct parts: The first chapter introduces the basic principles of Constraint Programming and provides a model of the constraints that are the most often encountered in scheduling problems. Chapters 2, 3, 4, and 5 are focused on the propagation of resource constraints, which usually are responsible for the "hardness" of the scheduling problem. Chapters 6, 7, and 8 are dedicated to the resolution of several scheduling problems. These examples illustrate the use and the practical efficiency of the constraint propagation methods of the previous chapters. They also show that besides constraint propagation, the exploration of the search space must be carefully designed, taking into account specific properties of the considered problem (e.g., dominance relations, symmetries, possible use of decomposition rules). Chapter 9 mentions various extensions of the model and presents promising research directions.

Constraints (Artificial intelligence) --- 658.513 --- Production scheduling --- 681.3*D1 --- Constraint satisfaction (Artificial intelligence) --- Artificial intelligence --- Job scheduling (Production control) --- Job-shop scheduling --- Project scheduling (Production control) --- Scheduling (Management) --- Production control --- Scheduling --- Supervision of production work. Follow-up, progressing, expediting. Scheduling --- Programming techniques--See also {681.3*E} --- 681.3*D1 Programming techniques--See also {681.3*E} --- 658.513 Supervision of production work. Follow-up, progressing, expediting. Scheduling --- Mathematical optimization. --- Operations research. --- Decision making. --- Computers. --- Calculus of variations. --- Optimization. --- Operations Research/Decision Theory. --- Theory of Computation. --- Calculus of Variations and Optimal Control; Optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis --- Decision making