Complementarity Problems: Examples and Preprocessing - Gams
Complementarity Problems: Examples and Preprocessing - Gams
Complementarity Problems: Examples and Preprocessing - Gams
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min<br />
NLP2MCP<br />
f ( x)<br />
s.<br />
t.<br />
g(<br />
x)<br />
≤ 0,<br />
r ≤ x ≤<br />
Introduce multipliers on constraints, form Lagrangian:<br />
L(x,? ) ≡ f(x) − λ′ g(<br />
x)<br />
Symbolic differentiation to create first-order optimality<br />
conditions automatically:<br />
⎡ ∇ L(<br />
x,<br />
λ)<br />
⎡∇<br />
− ′<br />
x ⎤ f ( x)<br />
λ ∇g(<br />
x)<br />
⎤<br />
F(<br />
x,<br />
λ)<br />
≡ ⎢ ⎥ = ⎢ ⎥<br />
⎣−<br />
∇λ<br />
L(<br />
x,<br />
λ)<br />
⎦ ⎣ g(<br />
x)<br />
⎦<br />
Small number of blocks of equations even for large problems<br />
F(x; õ) ? (x; õ) 2 [r; s] â [0; 1 )<br />
s
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