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interval list function ConstrainedMinimization ( inclusion function G, inclusion function H,
inclusion function F, interval A)
{ G is the inclusion function for a constraint function g. H is the inclusion function
for an solution acceptance set constraint function.
F is the inclusion function for the function f we want to minimize. }
begin
interval list S;
{ the solutions }
interval priority queue Q;
real
u;
{ upper bound }
interval
B, B 1 , B 2 ;
integer
i;
point
p ;
S := f ;
Q := CreateQueue ( A );
u := +•;
while not (Empty (Q)) do
begin
B := DeQueue (Q);
if H (B) = [1,1]
then Insert (B,S);
else
begin
Subdivide (B,B 1 ,B 2 );
{ Subdivides the interval B }
for i:=1 to 2 do
if (G (B i ) π [0,0]) and (lb (F (B i )) £ u) then
begin
EnQueue (B i ,Q); { based on lb (F (B i )) }
if HasIdentifiableFeasablePt (B i , p )
then u := min (u , f ( p ))
else if HasUnIdentifiableFeasablePt (B i )
then u := min (u , ub (F (B i )));
end
end
end ;
return S;
end ;
Algorithm 18.6.1.
The constrained minimization algorithm.
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