00483 ?a0a2174ee321f03b6f4c5f28194bec
An Algorithm and a Graphical Approach for Short Run Processes
END;
if abs(E)>0.0 then gamma:=A/E else gamma:=1.0; {*** self-scaling BFGS ***}
FOR I:=2 TO N IX) FOR J:=2 TO N DO
H[I,J]:=gamma*H[I,J]+(1.0+gamma*(E/A))*C[I,J]/A-gamma*((P[I]*D[J])+(B[I]*P[J]))/A;
END;
PROCEDURĘ RESTART;
VAR I,J:INTEGER;
BEGIN
FOR I:=2 TO N DO FOR J:=2 TO N DO IF I=J THEN H[I,J]:=1.0 ELSE H[I,J]:=0.0 END;
Function Findmaxstep(X,D:nx 1):extended; var i:integer,
Gmin,Gi:extended; be gin
Gmin:=le20; for i:=2 to n do begin
if D[i] < 0 then GI:=abs(LB[i]-X[i]) else GI:=abs(UB[i]-X(i]); if GKGmin then Gmin:=GI; end;
If Gmin>=le20 then Findmaxstep:=0.1 else Findmaxstep:=Gmin-DDelta; end;
PROCEDURĘ BFGS(VAR X:NXl;limit:integer); const max_it= 100;
VAR I,J,K:INTEGER; x_ant,P,Q,D,G:NXl;
Dnorm,Gmin,f_ant,FN,ALPHA:EXTENDED;
BEGIN
K:=0;it:=0;fti:=1 elOOO;
REPEAT
K:=K+1 ;it:=it+l ;f_ant:=fh;FN:=Fun(X);
IF it=l THEN BEGIN GRA(X);restart;END;
FOR I:=2 TO N DO BEGIN
x_ant[i]:=x[i];G[I]:=GRAD[I];D[I]:=0.0;
FOR J:=2 TO N DO D[I]:=D[I]-H[I,J]*GRAD(J];
END;
X_ANT[ 1 ]:=X[ 1 ];X_ANT[4]:=X[4];Gmin:=Findmaxstep(X,D);Dnorm:=norm(D); for i:=2 to n do d[i]:=d[i]*Gmin/Dnorm; {** normalize D to max step size **} ALPHA:=GOLDSTEIN_ARMIJO(FN,X,G,D);
FOR I:=2 TO N DO
BEGIN {**** Check bounds before moving **♦*}
IF p({I]+ALPHA*D[I]<=UB[I]) AND (X[I]+ALPHA*D[I]>=LB[I])
THEN X[I]:=X[I]+ALPHA*D[I]; P[I]:=ALPHA*D[I]
END;
GRA(X);FOR I;=2 TO N DO Q[I]:=GRAD[I]-G[I];
IF K=limit THEN begin k:=0; RESTART;end;
IF (ABS(NORM(X>NORM(x_ANT))>DDELTA) and (norm(p)*norm(q)<>0.0) THEN UPDATE_H(H,P,Q);
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