Decomposition
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Comments: Latex Typesetting Style, Recap: Primal Decomposition, Dual Decomposition, Dual Decomposition Algorithm, Finding Feasible Iterates, Interpretation, Decomposition With Constraints, Primal Decomposition (With Constraints) Algorithm, Example (Primal Decomposition With Constraints), Dual Decomposition (With Constraints), Dual Decomposition (With Constraints) Algorithm, General...more
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Recap: Ellipsoid Method, Improvements (To Ellipsoid Method), Proof Of Convergence, Interpretation Of Complexity, Deep Cut Ellipsoid Method, Ellipsoid Method With Deep Objective Cuts, Inequality Constrained Problems, Stopping Criterion, Epigraph Ellipsoid Method, Epigraph Ellipsoid Example, Summary: Methods For Handling, Nondifferentiable Convex Optimization Problems Directly, Decomposition...more
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Decomposition and abstraction through functions; introduction to recursion
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Decomposition Applications, Rate Control Setup, Rate Control Problem, Rate Control Lagrangian, Aside: Utility Functions, Rate Control Dual, Dual Decomposition Rate Control Algorithm, Generating Feasible Flows, Convergence Of Primal And Dual Objectives, Maximum Capacity Violation, Single Commodity Network Flow Setup, Network Flow Problem, Network Flow Lagrangian, Network Flow Dual,...more
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Karel and Java, Common Errors, Comments, Pre-conditions and Post-conditions, Decomposition, The DoubleBeepers Example, Importance of Good Software Engineering, The Right Decomposition, The CleanUpKarel Example
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Gain Of A Matrix In A Direction, Singular Value Decomposition, Interpretations, Singular Value Decomposition (SVD) Applications, General Pseudo-Inverse, Pseudo-Inverse Via Regularization, Full SVD, Image Of Unit Ball Under Linear Transformation, SVD In Estimation/Inversion, Sensitivity Of Linear Equations To Data Error
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Latent Semantic Indexing (LSI), Singular Value Decomposition (SVD) Implementation, Independent Component Analysis (ICA), The Application of ICA, Cumulative Distribution Function (CDF), ICA Algorithm, The Applications of ICA
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Professor Sylvia Ceyer covers radioactive decay and its various uses in modern medicine. Second order half-life, as a second order integrated rate law, is then discussed. The lecture concludes with the overlap of kinetics and chemical equilibrium: the equilibrium constant, elementary reactions, and an example, the decomposition of ozone.
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Orthonormal Set Of Vectors, Geometric Interpretation, Gram-Schmidt Procedure, General Gram-Schmidt Procedure, Applications Of Gram-Schmidt Procedure, 'Full' QR Factorization, Orthogonal Decomposition Induced By A, Least-Squares
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Seeing Functions as Data: Specific Plot Functions, Generic Plot Function, Back to the Set, Live Coding Example: Use of Set with User Defined Data Types, Client Callback Function, Review of the Classes Seen,5 Using Nested ADTs (Abstract Data Types), Live Coding Example, Recursion, Recursive Decomposition
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Continuation of Convex Optimization I. Topics include: Subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as...more
