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MGT-418: Convex optimization
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Lectures in this course (76)
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Convex Sets: MGT-418 Lecture
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On Convex Optimization covers course organization, mathematical optimization problems, solution concepts, and optimization methods.
Convex Functions: Theory and Applications
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Introduces convex functions, covering affine, convex, and conic hulls, transformations, inequalities, and conditions for convexity.
Max-Cut Problem: SDP Relaxation and Randomized Rounding
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Explores the Max-Cut Problem, its relaxation using SDP, and Polynomial Optimization.
Robust Optimization: Polynomial Approximation & Uncertainty Sets
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Explores robust optimization through polynomial approximation and uncertainty sets, including robust linear programs and optimization tricks.
Robust Optimization: Radiation Therapy & Support Vector Machines
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Explores robust optimization in radiation therapy and support vector machines, emphasizing worst-case scenarios and the use of linear decision rules.
Stochastic Optimization: Portfolio Optimization
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Explores stochastic optimization in portfolio management, emphasizing decision criteria for uncertain objectives and the concept of conditional value-at-risk.
Convex Functions: Theory and Applications
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Explores convex functions, affine transformations, pointwise maximum, minimization, Schur's Lemma, and relative entropy in mathematical optimization.
Convex Optimization Problems: Theory and Applications
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Explores convex optimization problems, optimality criteria, equivalent problems, and practical applications in transportation and robotics.
Lagrangian Duality: Theory and Applications
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Explores Lagrangian duality in convex optimization, discussing strong duality, dual solutions, and practical applications in second-order cone programs.
KKT Conditions: Convex Optimization
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Explores KKT conditions in convex optimization, covering dual cones, properties, generalized inequalities, and optimality conditions.
Conjugate Duality: Envelope Representations and Subgradients
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Explores envelope representations, subgradients, and the duality gap in convex optimization.
Optimization in Statistics and Machine Learning: Maximum Likelihood Estimation
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Explores maximum likelihood estimation, logistic regression, covariance estimation, and support vector machines for classification problems.
Convexifying Nonconvex Problems: SVM and Dimensionality Reduction
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Explores convexifying nonconvex problems through SVM and dimensionality reduction techniques.
Convex Relaxation in Optimization
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Explores convexifying nonconvex problems through relaxation techniques, illustrated with total variation reconstruction examples.
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