Page 206 - Compact Numerical Methods For Computers

Descent to a minimum I: variable metric algorithms 195

Algorithm 21. Variable metric minimiser (cont.)
end; {loop on i}
if D1>0 then {STEP 14} {test if update is possible}
begin {update}
D2:=0.0; {STEP 15 -- computation of B*y, yT*B*y}
for i:=1 to n do
begin
s:=0.0;
for j:=1 to n do s:=s+B[i, j]*c[j];
X[i]:=s; D2:=D2+s*c[i];
end; {loop on i}
D2:=1.0+D2/D1; {STEP 16 -- complete update}
for i:=1 to n do
begin
for j:=1 to n do
begin
B[i,j]:=B[i,j]-(t[i]*X[j]+X[i]*t[j]-D2*t[i]*t[j])/D1;
end; {loop on j}
end; {loop on i -- Update is now complete.}
end {update}
else
begin
writeln(‘ UPDATE NOT POSSIBLE*);
ilast:=gradcount; {to force a restart with B = l(n)}
end;
end {if count<n} {STEP 17}
else {count<n, cannot proceed}
begin
if ilast<gradcount then
begin
count:=0; {to force a steepest descent try}
ilast:=gradcount; {to reset to steepest descent search}
end; {if ilast}
end; {count=n}
end {if gradproj<0 ... do linear search}
else
begin
writeln(‘UPHILL SEARCH DIRECTION’);
ilast:=gradcount; {(to reset B to unit matrix}
count:=0; {to ensure we try again}
end,
until (count=n) and (ilast=gradcount);
end, {minimisation -- STEP 18}
{STEP 31 -- save best parameters and function value found}
writeln(‘Exiting from alg21.pas variable metric minimiser’);
writeln(‘ ‘, funcount,’ function evaluations used’);
writeln(‘ ‘, gradcount,’ gradient evaluations used’);
end; {alg21.pas == vmmin}