Review of Midterm 1

This blog will review the key concepts and theorem from previous section.

1. General form

2. Standard form

3. How to reformulate to standard form?

4. Convex/Concave function

5. affine function

6. Piece linear convex function

7. How to transform the piece linear function to linear programming problem

8. Transform the constaints like

   $$ \vert x_1 + \cdots + x_m \vert + \vert x_{m+1} +\cdots +x_n \vert \leq b $$

   which is equivalent to four linear inequlities as follow

   $$ \begin{equation} \begin{aligned} (x_1 +\cdots + x_m) + ( x_{m+1} + \cdots + x_n) &\leq b \\ -(x_1 + \cdots + x_m) + ( x_{m+1} + \cdots + x_n) &\leq b \\ (x_1 + \cdots + x_m) - ( x_{m+1} + \cdots + x_n) &\leq b \\ -(x_1 + \cdots + x_m) - ( x_{m+1} + \cdots + x_n) &\leq b \\ \end{aligned} \end{equation} $$

9. Transfer problem with absolute values

10. Solve ${ 2 }$-variables LO problem graphically

11. Polyhedron and Polyhedron in standard form representation

12. Convex set

13. Convex Combination and Convex hull

14. extrem point

15. vertex

16. Basic solution and Basic feasible solution

17. equivalent condition of basic solution

18. How to find basic solutions