| 週次 |
授課內容 |
| 第1週 |
Introduction: mathematical optimization; least squares and linear programing; convex |
| 第2週 |
Convex Sets: affine and convex sets; some important examples; operations that preserve convexity; generalized inequalities |
| 第3週 |
Convex Sets: separating and supporting hyperplanes, dual cones and generalized inequalities |
| 第4週 |
Convex Functions: basic properties and examples, operations that preserve convexity |
| 第5週 |
Convex Functions: The conjugate function, Quasi-convex functions, log-concave and log-convex functions; convexity with respect to generalized inequalities |
| 第6週 |
Convex Optimization Problems: optimization problems; convex optimization; linear optimization problems; |
| 第7週 |
Convex Optimization Problems: quadratic optimization problems; geometric programming; generalized inequality constraints; vector optimization |
| 第8週 |
Duality: the Lagrange dual function, the Lagrange dual problem |
| 第9週 |
midterm exam |
| 第10週 |
Duality: geometric interpretation; optimality conditions, examples |
| 第11週 |
Approximation and Fitting: norm-approximation; least-norm approximation; regularized approximation |
| 第12週 |
Approximation and Fitting: regularized approximation, robust approximation, function fitting and interpolation |
| 第13週 |
Statistical estimation: parametric distribution estimation; nonparametric distribution estimation |
| 第14週 |
Geometric problems: projection on a set; distance between sets; Euclidean distance and angle problems |
| 第15週 |
Geometric problems: extremal volume ellipsoids; centering; classification; placement and location; floor planning; |
| 第16週 |
Unconstrained minimization: unconstrained minimization problems; descent methods; newton’s method
Other more advanced topics in convex optimization
Solving homework problems |
自主學習
內容 |
02.閱覽產業及學術相關多媒體資料
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