Notation OR

2

3

4 Backgrounds

OR Convex sets Nonconvex set

OR x y z

7

8 Convex function

OR

10 : extreme points

OR Review-Linear Algebra

OR  Submatrices multiplication

OR  submatrix multiplications which will be frequently used.

OR

OR

OR Simultaneous Linear Equations

OR

OR

OR

OR Solving systems of linear equations (Gauss-Jordan Elimination, 변수의 치환 ) (will be used in the simplex method to solve LP problems)

OR  Infinitely many solutions case

OR

OR We have different basic solutions depending on which variables are considered as basic.

OR  Elementary row operations are equivalent to premultiplying a nonsingular square matrix to both sides of the equations

OR

OR

OR  So if we multiply all elementary row operation matrices, we get the matrix having the information about the elementary row operations we performed

OR

OR