00483 ?a0a2174ee321f03b6f4c5f28194bec

489

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);