Cours Programmation Linéaire et Recherche Opérationnelle

x1, x2, x3x4A B C D
Minimiser 2x1+ 2x2+x3+ 8x4
S.c
2x1+x2+x3≥12
3x1+ 4x2+ 3x3+ 5x4≥7
x1, x2, x3, x4≥0.

(P L)
Max z=f.x
S.c
Ax ≤b
x≥0.
f
A= (Aij )1≤i≤m
1≤j≤n∈Rmn
b= (bi)1≤i≤m
x= (xj)1≤j≤n∈Rn
K={x∈Rn, Ax =b, x ≥0}
KRnK
x∗∈Rnx∗
f(x∗)≥f(x),∀x∈K
x∗∈K x∗
v(P L) = f(x∗)
K=∅v(P L) = −∞
K v(P L)∈R∪+∞
K v(P L)=+∞
(P L)
Max z=f.x
S.c
Ax =b
x≥0.
i∈ {1,2, ..., m}Aix=bi⇔Aix≤bi
Aix≥bi.