Linear functions:
f(x1, x2) = 2x1 + 3x2,
f(x1, x2, x3) = 3x1 + 5x2 - x3
Nonlinear functions:
f(x1, x2) = 2(x1^2) - (5^x2)
f(x1, x2, x3) = sin(x1) + 5x2 - (1/(x^5))
LP formulations
- standard form (equality constraints) :
minimize z = cx,
subject to Ax = b,
x >= 0,
- canonical forms for minimization and maximization problems (inequality constraints) :
minimize z = cx, maximize z = cx,
subject to Ax >= b, subject to Ax <= b,
x >= 0, x >= 0.
Convert the Canonical Form to the Standard Form
- using Slack variable
Ax <= b
x >= 0
↓
Ax + x1 = b
x , x1 >= 0
- using Surplus variable
Ax >= b
x >= 0
↓
Ax - x1 = b
x , x1 >= 0
(한글 버전)
Acknowledgement
본 자료는 UNIST 권상진 교수 및 펜실베니아 주립대 Jose A. Ventura 교수의 강의자료를 일부 수정한 것임을 밝힙니다.
(영어 버전)
Acknowledgement
I would like to acknowledge the support of Dr. Sang Jin Kweon at UNIST and Dr. Jose A. Ventura at Pennsylvania State University in sharing the course material.