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Emphasizing practical understanding over the technicalities of specific algorithms, this elegant textbook is an accessible introduction to the field of optimization, focusing on powerful and reliable convex optimization techniques. Students and practitioners will learn how to recognize, simplify, model and solve optimization problems - and apply these principles to their own projects. A clear and self-contained introduction to linear algebra demonstrates core mathematical concepts in a way that is easy to follow, and helps students to understand their practical relevance. Requiring only a basic understanding of geometry, calculus, probability and statistics, and striking a careful balance between accessibility and rigor, it enables students to quickly understand the material, without being overwhelmed by complex mathematics. Accompanied by numerous end-of-chapter problems, an online solutions manual for instructors, and relevant examples from diverse fields including engineering, data science, economics, finance, and management, this is the perfect introduction to optimization for undergraduate and graduate students.
Mathematical optimization. --- Convex sets. --- Convex functions.
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Control theory. --- Matrix inequalities. --- Mathematical optimization. --- Control theory --- Matrix inequalities --- Mathematical optimization --- #TELE:SISTA --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Inequalities (Mathematics) --- Matrices --- Dynamics --- Machine theory
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Control theory. --- Matrix inequalities. --- Mathematical optimization. --- Théorie de la commande --- Inégalités matricielles --- Optimisation mathématique --- Matrix inequalities --- Control theory --- Mathematical optimization --- Inequalities (Mathematics) --- Matrices --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Dynamics --- Machine theory
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Robust optimization is a fairly 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. The authors are the principal developers of robust optimization.
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.
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