1. |
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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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2. |
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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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3. |
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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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4. |
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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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5. |
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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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6. |
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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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7. |
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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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8. |
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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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9. |
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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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10. |
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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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11. |
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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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12. |
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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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13. |
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CH9: Approximation and fitting |
1. Signal reconstruction; 2. Quadratic smoothing example; 3. Total variation reconstruction example |
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14. |
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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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15. |
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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 |
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