The Convex Optimization foundation of machine learning

2015-09-09 the convex optimization bought today just arrived. Start learning some basic concepts from today. I don't know if I can learn and solve the actual problem in 2 years ' time.

The linear function needs to satisfy the equation strictly, and the convex function only needs to satisfy the inequality in A and b given the specific merits. Therefore, the linear programming problem is also a convex optimization problem, and the convex optimization can be regarded as the extension of linear programming.

1. Radiation set

Definition: The line of any two points in a set of C is within the set C, then the set C is an affine set.

Example: Straight, flat, super plane

2. Imitation Injection bag

Definition: Contains the smallest affine set of Set C.

Affine dimension: The dimension of the affine package.

The affine dimension of the triangle is 2.

The number of affine dimensions for a segment is 1.

The affine dimension of the ball is 3.

3. Convex set

Definition: The segment of any two points within a set C is within the set C, then the set C is a convex set.

4. Relation of affine sets and convex sets

Because the conditions of affine sets are stronger than those of convex sets, affine sets are necessarily convex sets.

5. Convex Package:

The most convex set containing the set C is called the convex hull of the set C

6. Cone (Cones)

Example of a cone: The ray, the Ray family, the angle of the origin.

7. Cone Bag

8. Ultra-planar and half-space

Super plane: Hyperplane

Half-space halfspace:

9. European Ball and ellipsoid

European ball:

Ellipsoid:

10. Norm Sphere and norm cone (extension of European space)

Norm:

Norm Sphere:

Norm Cone:

The Convex Optimization foundation of machine learning