Convex Optimization Course Slides Notes
1. convex set
1.1. classes of convex set
Def: convex set
Example:
Def: conv
1.1.1. affine set
Def: affine set (lines)
Note: dim > 1
Note: other def
Example:
Def: aff
Def: aff dim
Def: relint and cl
1.1.2. convex hull
Def: convex hull
Example:
1.1.2.1. norm hull
Def:
1.1.3. hyperplane
Def: hyperplane
1.1.3.1. positive hull
Def:
1.1.4. half space
Def:
1.1.5. Euclid ball
Def:
1.1.6. ellipsoid
Def:
1.1.7. polyhedral
Def:
Note:
1.1.7.1. singleton
Def:
1.2. convex operations
1.2.1. intersection
Def:
1.2.2. affine functions
Def:
Example:
Example:
Example:
1.2.3. perspective function
Def:
Note:
Note:
1.2.4. linear
Def:
Note:
2. convex function
Def:
Example:
Example:
Example:
P67
Qua: necc & suff
first condition
Note: first condition
second condition
2.1. induced sets
2.1.1. sublevel set
Def:
Qua: => convex
2.1.2. epigraph
Def:
Qua: necc & suff
2.2. induced functions
2.2.1. conjugate function
Def：
Qua: convex
Qua:
Qua:
Qua: =>
Qua:
Qua:
2.3. convex operations
2.3.1. sum of positive weight
- Def:
2.3.2. affine function
Def:
2.3.3. point-wise max
Def:
Note: generalization
2.3.4. combinations
Def:
see p81
2.3.5. min
Def:
2.3.6. projection
Def:
3. convex problem
4. convex solving
4.1. =+>
4.1.1. KKT
4.1.2. Barrier Method
4.1.3. Primal Dual method
4.1.4. Linear Programming
##=
4.1.5. problem attributes
4.1.6. newton descent
4.1.7. improved newton
4.2. no constraint
4.2.1. problem attributes
4.2.2. general descent
4.2.3. gradient descent
4.2.4. steepest descent
###newton descent
