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Cet ouvrage prsente les concepts fondamentaux d'optimisation classique et de programmation linaire. Outre un prologue et un pilogue, l'ouvrage comporte une partie de thorie mathematique sur le calcul matriciel et les syst mes d'quations et d'inquations linaires. Il traite ensuite d'optimisation classique avec et sans contraintes, de programmation linaire, de la mthode du simplexe et du simplexe rvis. Les derniers chapitres sont consacrs la dualit, la post-optimisation et analyse de sensibilit ainsi qu'aux probl mes de transport. L'accent a t mis sur l'explication des mthodes exposes et leur uti

Mathematical optimization --- Linear programming --- Optimisation mathématique --- Programmation linéaire --- Mathematical optimization. --- Linear programming. --- Optimisation mathématique --- Programmation linéaire --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Production scheduling --- Programming (Mathematics) --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis

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Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.

Robust optimization. --- Linear programming. --- 519.8 --- 681.3*G16 --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 519.8 Operational research --- Operational research --- Robust optimization --- Linear programming --- Optimisation robuste --- Programmation linéaire --- Optimization, Robust --- RO (Robust optimization) --- Mathematical optimization --- Production scheduling --- Programming (Mathematics) --- 0O. --- Accuracy and precision. --- Additive model. --- Almost surely. --- Approximation algorithm. --- Approximation. --- Best, worst and average case. --- Bifurcation theory. --- Big O notation. --- Candidate solution. --- Central limit theorem. --- Chaos theory. --- Coefficient. --- Computational complexity theory. --- Constrained optimization. --- Convex hull. --- Convex optimization. --- Convex set. --- Cumulative distribution function. --- Curse of dimensionality. --- Decision problem. --- Decision rule. --- Degeneracy (mathematics). --- Diagram (category theory). --- Duality (optimization). --- Dynamic programming. --- Exponential function. --- Feasible region. --- Floor and ceiling functions. --- For All Practical Purposes. --- Free product. --- Ideal solution. --- Identity matrix. --- Inequality (mathematics). --- Infimum and supremum. --- Integer programming. --- Law of large numbers. --- Likelihood-ratio test. --- Linear dynamical system. --- Linear inequality. --- Linear map. --- Linear matrix inequality. --- Linear regression. --- Loss function. --- Margin classifier. --- Markov chain. --- Markov decision process. --- Mathematical optimization. --- Max-plus algebra. --- Maxima and minima. --- Multivariate normal distribution. --- NP-hardness. --- Norm (mathematics). --- Normal distribution. --- Optimal control. --- Optimization problem. --- Orientability. --- P versus NP problem. --- Pairwise. --- Parameter. --- Parametric family. --- Probability distribution. --- Probability. --- Proportionality (mathematics). --- Quantity. --- Random variable. --- Relative interior. --- Robust control. --- Robust decision-making. --- Semi-infinite. --- Sensitivity analysis. --- Simple set. --- Singular value. --- Skew-symmetric matrix. --- Slack variable. --- Special case. --- Spherical model. --- Spline (mathematics). --- State variable. --- Stochastic calculus. --- Stochastic control. --- Stochastic optimization. --- Stochastic programming. --- Stochastic. --- Strong duality. --- Support vector machine. --- Theorem. --- Time complexity. --- Uncertainty. --- Uniform distribution (discrete). --- Unimodality. --- Upper and lower bounds. --- Variable (mathematics). --- Virtual displacement. --- Weak duality. --- Wiener filter. --- With high probability. --- Without loss of generality.