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CH 1: The introduction of this course and basic concepts | The schedule for this semester. Reference book, requirments and evaluation method, some basic concepts | ![]() |
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CH 2: Convex sets | 1.affine and convex sets; 2. some important examples; 3. Operations that preserve convexity; 4. Separating and supporting hyperplanes | ![]() |
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CH 3: Convex functions | 1. basic properties and examples; 2.operations that preserve convexity; 3. | ![]() |
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CH 3: Convex functions | 1.operations that preserve convexity; 2. Jensens inequality; 3. conjugate functions | ![]() |
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Ch4: Convex optimization problems | 1. Optimization problems in standard form; 2. Convex optimization problem; | ![]() |
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Ch4: Convex optimization problems | 1. Convex optimization problem; 2. equivalent convex problems | ![]() |
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Ch4: Convex optimization problems; CH5: Duality | 1. Linear program; 2. QCQP; 3.second order cone programming; 4: Lagrange dual function; 5: Standard form Lp | ![]() |
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CH5: Duality | 1: Lagrange dual problem; 2: weak and strong duality | ![]() |
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CH5: Duality | 1: Geometric interpretation; | ![]() |
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CH5: Duality | 1. Slaters constraint equation; 2. KKT conditions | ![]() |
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CH5: Duality | 1. Saddle point interpretation; 2. Perturbation and sensitivity analysis | ![]() |
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CH5: Duality; CH6: Unconstrained minimization | 1. Problem reformulations; 2. Strong convexity and implications | ![]() |
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CH6: Unconstrained minimization | 1. Descent methods; 2. linear search types; 3. Gradient descent method | ![]() |
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CH6: Unconstrained minimization | 1. Quadratic problem example; 2. Nonquadratic problem example; 3. Steeppest descent method | ![]() |
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CH6: Unconstrained minimization | 1. Different norm in normalized steepest descent method; 2. Choice of norm; | ![]() |
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CH6: Unconstrained minimization | 1. Newton step; 2. Newton decrement | ![]() |
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CH6: Unconstrained minimization | 1. Newton method; 2. Classical convergence analysis | ![]() |
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CH6: Unconstrained minimization | 1. Classical convergence analysis; 2. Damped Newton phase; 3. Implementation | ![]() |
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CH7: Equality constrained minimization | 1. Equality constrained minimization; 2. Quadratic minimization | ![]() |
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CH7: Equality constrained minimization | 1. Quadratic minimization; 2. Eliminating equality constraints; 3. Example | ![]() |
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CH7: Equality constrained minimization | 1. Newton step; 2. Newton decrement; 3. Newton method with equality constraints; 4. Newton method and elimination; 5. Newton step at infeasible points | ![]() |
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CH7: Equality constrained minimization | 1. Infeasible start Newton method; 2. Solving KKT system; 3.Analytic centering | ![]() |
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CH8: Iterior Point Method | 1. Inequality constrained minimization; 2. Logrithmic barrier; 3. Central path | ![]() |
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CH8: Iterior Point Method | 1. Dual points on central path; 2. Interpretation via KKT conditions; 3. Force field interpretation; 4. Barrier method; 5. Convergence analysis | ![]() |
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CH8: Iterior Point Method | 1. Barrier method; 2. Convergence analysis; 3. Feasibility and phase I methods | ![]() |
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CH8: Iterior Point Method | 1. Primal-dual interior point methods; 2. Interpretation of Newton step | ![]() |
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CH8: Iterior Point Method | 1. L1 norm approximation | ![]() |
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CH9: Approximation and fitting | 1. Norm approximation; 2. Penalty function approximation | ![]() |
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CH9: Approximation and fitting | 1. Example; 2. Huber penaltry function; 3. Least norm problems | ![]() |
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CH9: Approximation and fitting | 1. Signal reconstruction; 2. Quadratic smoothing example; 3. Total variation reconstruction example | ![]() |
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CH9: Statistical estimation | 1. Maximum likelihood estimation; 2. Linear measurments wkth IID noise; 3. Exampes | ![]() |
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CH9: Statistical estimation | 1. Homework 3 comments; 2. Final project explanation | ![]() |
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CH9: Statistic estimation; Geometric problems; Penalty barrier and augmented Lagrangian methods | 1. Logistic regression; 2. Linear discrimination; 3. Roboust linear discrimination; 4. Quadratic penalty method | ![]() |
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CH9: Penalty barrier and augmented Lagrangian methods | 1. Augmented Lagrangian method; 2. L1 penlaty function | ![]() |