--- /dev/null
+***********************************************************************
+* *
+* PLIP - A LIMITED MEMORY VARIABLE METRIC ALGORITHM FOR *
+* LARGE-SCALE OPTIMIZATION. *
+* *
+***********************************************************************
+
+
+1. Introduction:
+----------------
+
+ The double-precision FORTRAN 77 basic subroutine PLIP is designed
+to find a close approximation to a local minimum of a nonlinear
+function F(X) with simple bounds on variables. Here X is a vector of NF
+variables and F(X) is a smooth function. We suppose that NF is large
+but the sparsity pattern of the Hessian matrix is not known (or the
+Hessian matrix is dense). Simple bounds are assumed in the form
+
+ X(I) unbounded if IX(I) = 0,
+ XL(I) <= X(I) if IX(I) = 1,
+ X(I) <= XU(I) if IX(I) = 2,
+ XL(I) <= X(I) <= XU(I) if IX(I) = 3,
+ XL(I) = X(I) = XU(I) if IX(I) = 5,
+
+where 1 <= I <= NF. To simplify user's work, two additional easy to use
+subroutines are added. They call the basic general subroutine PLIP:
+
+ PLIPU - unconstrained large-scale optimization,
+ PLIPS - large-scale optimization with simple bounds.
+
+All subroutines contain a description of formal parameters and
+extensive comments. Furthermore, two test programs TLIPU and TLIPS are
+included, which contain several test problems (see e.g. [2]). These
+test programs serve as examples for using the subroutines, verify their
+correctness and demonstrate their efficiency.
+ In this short guide, we describe all subroutines which can be
+called from the user's program. A detailed description of the method is
+given in [1]. In the description of formal parameters, we introduce a
+type of the argument that specifies whether the argument must have a
+value defined on entry to the subroutine (I), whether it is a value
+which will be returned (O), or both (U), or whether it is an auxiliary
+value (A). Note that the arguments of the type I can be changed on
+output under some circumstances, especially if improper input values
+were given. Besides formal parameters, we can use a COMMON /STAT/ block
+containing statistical information. This block, used in each subroutine
+has the following form:
+
+ COMMON /STAT/ NRES,NDEC,NIN,NIT,NFV,NFG,NFH
+
+The arguments have the following meaning:
+
+ Argument Type Significance
+ ----------------------------------------------------------------------
+ NRES O Positive INTEGER variable that indicates the number of
+ restarts.
+ NDEC O Positive INTEGER variable that indicates the number of
+ matrix decompositions.
+ NIN O Positive INTEGER variable that indicates the number of
+ inner iterations (for solving linear systems).
+ NIT O Positive INTEGER variable that indicates the number of
+ iterations.
+ NFV O Positive INTEGER variable that indicates the number of
+ function evaluations.
+ NFG O Positive INTEGER variable that specifies the number of
+ gradient evaluations.
+ NFH O Positive INTEGER variable that specifies the number of
+ Hessian evaluations.
+
+
+2. Subroutines PLIPU, PLIPS:
+----------------------------
+
+The calling sequences are
+
+ CALL PLIPU(NF,X,IPAR,RPAR,F,GMAX,IPRNT,ITERM)
+ CALL PLIPS(NF,X,IX,XL,XU,IPAR,RPAR,F,GMAX,IPRNT,ITERM)
+
+The arguments have the following meaning.
+
+ Argument Type Significance
+ ----------------------------------------------------------------------
+ NF I Positive INTEGER variable that specifies the number of
+ variables of the objective function.
+ X(NF) U On input, DOUBLE PRECISION vector with the initial
+ estimate to the solution. On output, the approximation
+ to the minimum.
+ IX(NF) I On input (significant only if NB>0) INTEGER vector
+ containing the simple bounds types:
+ IX(I)=0 - the variable X(I) is unbounded,
+ IX(I)=1 - the lower bound X(I) >= XL(I),
+ IX(I)=2 - the upper bound X(I) <= XU(I),
+ IX(I)=3 - the two side bound XL(I) <= X(I) <= XU(I),
+ IX(I)=5 - the variable X(I) is fixed (given by its
+ initial estimate).
+ XL(NF) I DOUBLE PRECISION vector with lower bounds for variables
+ (significant only if NB>0).
+ XU(NF) I DOUBLE PRECISION vector with upper bounds for variables
+ (significant only if NB>0).
+ IPAR(7) I INTEGER parameters:
+ IPAR(1)=MIT, IPAR(2)=MFV, IPAR(3)-NONE,
+ IPAR(4)=IEST, IPAR(5)-MET, IPAR(6)-NONE,
+ IPAR(7)=MF.
+ Parameters MIT, MFV, IEST, MET, MF are described
+ in Section 3 together with other parameters of the
+ subroutine PLIP.
+ RPAR(9) I DOUBLE PRECISION parameters:
+ RPAR(1)=XMAX, RPAR(2)=TOLX, RPAR(3)=TOLF,
+ RPAR(4)=TOLB, RPAR(5)=TOLG, RPAR(6)=FMIN,
+ RPAR(7)-NONE, RPAR(6)-NONE, RPAR(9)-NONE.
+ Parameters XMAX, TOLX, TOLF, TOLB, TOLG, FMIN are
+ described in Section 3 together with other parameters
+ of the subroutine PLIP.
+ F O DOUBLE PRECISION value of the objective function at the
+ solution X.
+ GMAX O DOUBLE PRECISION maximum absolute value of a partial
+ derivative of the Lagrangian function.
+ IPRNT I INTEGER variable that specifies PRINT:
+ IPRNT= 0 - print is suppressed,
+ IPRNT= 1 - basic print of final results,
+ IPRNT=-1 - extended print of final results,
+ IPRNT= 2 - basic print of intermediate and final
+ results,
+ IPRNT=-2 - extended print of intermediate and final
+ results.
+ ITERM O INTEGER variable that indicates the cause of termination:
+ ITERM= 1 - if |X - XO| was less than or equal to TOLX
+ in two subsequent iterations,
+ ITERM= 2 - if |F - FO| was less than or equal to TOLF
+ in two subsequent iterations,
+ ITERM= 3 - if F is less than or equal to TOLB,
+ ITERM= 4 - if GMAX is less than or equal to TOLG,
+ ITERM= 6 - if termination criterion was not satisfied,
+ but the solution is probably acceptable,
+ ITERM=11 - if NIT exceeded MIT,
+ ITERM=12 - if NFV exceeded MFV,
+ ITERM< 0 - if the method failed.
+
+ The subroutines PLIPU, PLIPS require the user supplied subroutines
+OBJ and DOBJ that define the objective function and its gradient and
+have the form
+
+ SUBROUTINE OBJ(NF,X,F)
+ SUBROUTINE DOBJ(NF,X,G)
+
+The arguments of the user supplied subroutines have the following
+meaning.
+
+ Argument Type Significance
+ ----------------------------------------------------------------------
+ NF I Positive INTEGER variable that specifies the number of
+ variables of the objective function.
+ X(NF) I DOUBLE PRECISION an estimate to the solution.
+ F O DOUBLE PRECISION value of the objective function at the
+ point X.
+ G(NF) O DOUBLE PRECISION gradient of the objective function
+ at the point X.
+
+
+3. Subroutine PLIP:
+-------------------
+
+ This general subroutine is called from all subroutines described
+in Section 2. The calling sequence is
+
+ CALL PLIP(NF,NB,X,IX,XL,XU,GF,S,XO,GO,SO,XM,XR,GR,XMAX,TOLX,TOLF,
+ & TOLB,TOLG,FMIN,GMAX,F,MIT,MFV,IEST,MET,MF,IPRNT,ITERM)
+
+The arguments NF, NB, X, IX, XL, XU, GMAX, F, IPRNT, ITERM, have the
+same meaning as in Section 2. Other arguments have the following meaning:
+
+ Argument Type Significance
+ ----------------------------------------------------------------------
+ GF(NF) A DOUBLE PRECISION gradient of the objective function.
+ S(NF) A DOUBLE PRECISION direction vector.
+ XO(NF) A DOUBLE PRECISION array which contains increments of
+ variables.
+ GO(NF) A DOUBLE PRECISION array which contains increments of
+ gradients.
+ SO(NF) A DOUBLE PRECISION auxiliary array.
+ XM(NF*MF) A DOUBLE PRECISION array which contains columns
+ of the updated matrix stored in the product form.
+ XR(MF) A DOUBLE PRECISION array which contains reduced
+ increments of variables.
+ GR(MF) A DOUBLE PRECISION array which contains reduced
+ increments of gradients.
+ XMAX I DOUBLE PRECISION maximum stepsize; the choice XMAX=0
+ causes that the default value 1.0D+16 will be taken.
+ TOLX I DOUBLE PRECISION tolerance for the change of the
+ coordinate vector X; the choice TOLX=0 causes that the
+ default value TOLX=1.0D-16 will be taken.
+ TOLF I DOUBLE PRECISION tolerance for the change of function
+ values; the choice TOLF=0 causes that the default
+ value TOLF=1.0D-14 will be taken.
+ TOLB I DOUBLE PRECISION minimum acceptable function value;
+ the choice TOLB=0 causes that the default value
+ TOLB=FMIN+1.0D-16 will be taken.
+ TOLG I DOUBLE PRECISION tolerance for the Lagrangian function
+ gradient; the choice TOLG=0 causes that the default
+ value TOLG=1.0D-6 will be taken.
+ FMIN I DOUBLE PRECISION lower bound for the minimum function
+ value.
+ MIT I INTEGER variable that specifies the maximum number of
+ iterations; the choice MIT=0 causes that the default
+ value 9000 will be taken.
+ MFV I INTEGER variable that specifies the maximum number of
+ function evaluations; the choice MFV=0 causes that
+ the default value 9000 will be taken.
+ IEST I INTEGER estimation of the minimum functiom value for
+ the line search:
+ IEST=0 - estimation is not used,
+ IEST=1 - lower bound FMIN is used as an estimation
+ for the minimum function value.
+ MET I INTEGER variable that specifies the limited-memory
+ method:
+ MET=1 - rank-one method,
+ MET=2 - rank-two method.
+ The choice MET=0 causes that the default value MET=2
+ will be taken.
+ MF I The number of limited-memory variable metric updates
+ in each iteration (they use MF stored vectors).
+
+The choice of parameter XMAX can be sensitive in many cases. First, the
+objective function can be evaluated only in a relatively small region
+(if it contains exponentials) so that the maximum stepsize is necessary.
+Secondly, the problem can be very ill-conditioned far from the solution
+point so that large steps can be unsuitable. Finally, if the problem has
+more local solutions, a suitably chosen maximum stepsize can lead to
+obtaining a better local solution.
+ The subroutine PLIP requires the user supplied subroutines OBJ
+and DOBJ which are described in Section 2.
+
+4. Verification of the subroutines:
+-----------------------------------
+
+ Subroutine PLIPU can be verified and tested using the program
+TLIPU. This program calls the subroutines TIUD14 (initiation), TFFU14
+(function evaluation) and TFGU14 (gradient evaluation) containing
+22 unconstrained test problems with at most 1000 variables [2]. The
+results obtained by the program TLIPU on a PC computer with Microsoft
+Power Station Fortran compiler have the following form.
+
+NIT= 5383 NFV= 5417 NFG= 5417 F= 0.601022658E-13 G= 0.599E-06 ITERM= 4
+NIT= 530 NFV= 557 NFG= 557 F= 3.57276719 G= 0.124E-05 ITERM= 2
+NIT= 125 NFV= 128 NFG= 128 F= 0.338270284E-12 G= 0.518E-06 ITERM= 4
+NIT= 109 NFV= 114 NFG= 114 F= 269.499543 G= 0.669E-06 ITERM= 4
+NIT= 26 NFV= 27 NFG= 27 F= 0.710072396E-11 G= 0.951E-06 ITERM= 4
+NIT= 35 NFV= 36 NFG= 36 F= 0.142942272E-10 G= 0.737E-06 ITERM= 4
+NIT= 36 NFV= 41 NFG= 41 F= 336.937181 G= 0.956E-06 ITERM= 4
+NIT= 33 NFV= 36 NFG= 36 F= 761774.954 G= 0.192E-02 ITERM= 2
+NIT= 15 NFV= 18 NFG= 18 F= 316.436141 G= 0.264E-06 ITERM= 4
+NIT= 2003 NFV= 2030 NFG= 2030 F= -124.950000 G= 0.116E-04 ITERM= 2
+NIT= 157 NFV= 175 NFG= 175 F= 10.7765879 G= 0.299E-06 ITERM= 4
+NIT= 337 NFV= 350 NFG= 350 F= 982.273617 G= 0.145E-04 ITERM= 2
+NIT= 9 NFV= 10 NFG= 10 F= 0.230414406E-14 G= 0.642E-07 ITERM= 4
+NIT= 8 NFV= 10 NFG= 10 F= 0.128834241E-08 G= 0.977E-06 ITERM= 4
+NIT= 1226 NFV= 1256 NFG= 1256 F= 1.92401599 G= 0.970E-06 ITERM= 4
+NIT= 237 NFV= 246 NFG= 246 F= -427.404476 G= 0.501E-04 ITERM= 2
+NIT= 598 NFV= 604 NFG= 604 F=-0.379921091E-01 G= 0.908E-06 ITERM= 4
+NIT= 989 NFV= 998 NFG= 998 F=-0.245741193E-01 G= 0.975E-06 ITERM= 4
+NIT= 1261 NFV= 1272 NFG= 1272 F= 59.5986241 G= 0.410E-05 ITERM= 2
+NIT= 2045 NFV= 2058 NFG= 2058 F= -1.00013520 G= 0.911E-06 ITERM= 4
+NIT= 2175 NFV= 2196 NFG= 2196 F= 2.13866377 G= 0.996E-06 ITERM= 4
+NIT= 1261 NFV= 1292 NFG= 1292 F= 1.00000000 G= 0.927E-06 ITERM= 4
+NITER =18598 NFVAL =18871 NSUCC = 22
+TIME= 0:00:10.63
+
+The rows corresponding to individual test problems contain the number of
+iterations NIT, the number of function evaluations NFV, the number of
+gradient evaluations NFG, the final value of the objective function F,
+the norm of gradient G and the cause of termination ITERM.
+ Subroutine PLIPS can be verified and tested using the program
+TLIPS. This program calls the subroutines TIUD14 (initiation), TFFU14
+(function evaluation), TFGU14 (gradient evaluation) containing 22 box
+constrained test problems with at most 1000 variables [2]. The results
+obtained by the program TLIPS on a PC computer with Microsoft Power
+Station Fortran compiler have the following form.
+
+NIT= 5263 NFV= 5321 NFG= 5321 F= 0.530131995E-13 G= 0.370E-05 ITERM= 2
+NIT= 2293 NFV= 2447 NFG= 2447 F= 3930.43962 G= 0.251E-04 ITERM= 2
+NIT= 127 NFV= 132 NFG= 132 F= 0.210550150E-12 G= 0.437E-06 ITERM= 4
+NIT= 70 NFV= 72 NFG= 72 F= 269.522686 G= 0.794E-06 ITERM= 4
+NIT= 26 NFV= 27 NFG= 27 F= 0.710072396E-11 G= 0.951E-06 ITERM= 4
+NIT= 35 NFV= 36 NFG= 36 F= 0.142942272E-10 G= 0.737E-06 ITERM= 4
+NIT= 37 NFV= 43 NFG= 43 F= 336.937181 G= 0.133E-05 ITERM= 2
+NIT= 59 NFV= 65 NFG= 65 F= 761925.725 G= 0.399E-03 ITERM= 2
+NIT= 508 NFV= 510 NFG= 510 F= 428.056916 G= 0.776E-06 ITERM= 4
+NIT= 1253 NFV= 1277 NFG= 1277 F= -82.5400568 G= 0.120E-04 ITERM= 2
+NIT= 13 NFV= 19 NFG= 19 F= 96517.2947 G= 0.150E-04 ITERM= 2
+NIT= 95 NFV= 102 NFG= 102 F= 4994.21410 G= 0.790E-04 ITERM= 2
+NIT= 9 NFV= 10 NFG= 10 F= 0.230414406E-14 G= 0.642E-07 ITERM= 4
+NIT= 8 NFV= 10 NFG= 10 F= 0.128834241E-08 G= 0.977E-06 ITERM= 4
+NIT= 1226 NFV= 1256 NFG= 1256 F= 1.92401599 G= 0.970E-06 ITERM= 4
+NIT= 227 NFV= 228 NFG= 228 F= -427.391653 G= 0.952E-05 ITERM= 2
+NIT= 598 NFV= 604 NFG= 604 F=-0.379921091E-01 G= 0.908E-06 ITERM= 4
+NIT= 989 NFV= 998 NFG= 998 F=-0.245741193E-01 G= 0.975E-06 ITERM= 4
+NIT= 1367 NFV= 1383 NFG= 1383 F= 1654.94525 G= 0.105E-04 ITERM= 2
+NIT= 2274 NFV= 2303 NFG= 2303 F= -1.00013520 G= 0.798E-06 ITERM= 4
+NIT= 1196 NFV= 1211 NFG= 1211 F= 2.41354873 G= 0.975E-06 ITERM= 4
+NIT= 1361 NFV= 1381 NFG= 1381 F= 1.00000000 G= 0.962E-06 ITERM= 4
+NITER =19034 NFVAL =19435 NSUCC = 22
+TIME= 0:00:11.09
+
+References:
+-----------
+
+[1] Luksan L., Matonoha C., Vlcek J.: LSA: Algorithms for large-scale
+ unconstrained and box constrained optimization Technical Report V-896.
+ Prague, ICS AS CR, 2004.
+
+[2] Luksan L., Vlcek J.: Sparse and partially separable test problems
+ for unconstrained and equality constrained optimization. Research
+ Report V-767, Institute of Computer Science, Academy of Sciences
+ of the Czech Republic, Prague, Czech Republic, 1998.
+\1a
--- /dev/null
+***********************************************************************
+* *
+* PNET - A LIMITED MEMORY VARIABLE METRIC ALGORITHM FOR *
+* LARGE-SCALE OPTIMIZATION. *
+* *
+***********************************************************************
+
+
+1. Introduction:
+----------------
+
+ The double-precision FORTRAN 77 basic subroutine PNET is designed
+to find a close approximation to a local minimum of a nonlinear
+function F(X) with simple bounds on variables. Here X is a vector of NF
+variables and F(X) is a smooth function. We suppose that NF is large
+but the sparsity pattern of the Hessian matrix is not known (or the
+Hessian matrix is dense). Simple bounds are assumed in the form
+
+ X(I) unbounded if IX(I) = 0,
+ XL(I) <= X(I) if IX(I) = 1,
+ X(I) <= XU(I) if IX(I) = 2,
+ XL(I) <= X(I) <= XU(I) if IX(I) = 3,
+ XL(I) = X(I) = XU(I) if IX(I) = 5,
+
+where 1 <= I <= NF. To simplify user's work, two additional easy to use
+subroutines are added. They call the basic general subroutine PNET:
+
+ PNETU - unconstrained large-scale optimization,
+ PNETS - large-scale optimization with simple bounds.
+
+All subroutines contain a description of formal parameters and
+extensive comments. Furthermore, two test programs TNETU and TNETS are
+included, which contain several test problems (see e.g. [2]). These
+test programs serve as examples for using the subroutines, verify their
+correctness and demonstrate their efficiency.
+ In this short guide, we describe all subroutines which can be
+called from the user's program. A detailed description of the method is
+given in [1]. In the description of formal parameters, we introduce a
+type of the argument that specifies whether the argument must have a
+value defined on entry to the subroutine (I), whether it is a value
+which will be returned (O), or both (U), or whether it is an auxiliary
+value (A). Note that the arguments of the type I can be changed on
+output under some circumstances, especially if improper input values
+were given. Besides formal parameters, we can use a COMMON /STAT/ block
+containing statistical information. This block, used in each subroutine
+has the following form:
+
+ COMMON /STAT/ NRES,NDEC,NIN,NIT,NFV,NFG,NFH
+
+The arguments have the following meaning:
+
+ Argument Type Significance
+ ----------------------------------------------------------------------
+ NRES O Positive INTEGER variable that indicates the number of
+ restarts.
+ NDEC O Positive INTEGER variable that indicates the number of
+ matrix decompositions.
+ NIN O Positive INTEGER variable that indicates the number of
+ inner iterations (for solving linear systems).
+ NIT O Positive INTEGER variable that indicates the number of
+ iterations.
+ NFV O Positive INTEGER variable that indicates the number of
+ function evaluations.
+ NFG O Positive INTEGER variable that specifies the number of
+ gradient evaluations.
+ NFH O Positive INTEGER variable that specifies the number of
+ Hessian evaluations.
+
+
+2. Subroutines PNETU, PNETS:
+----------------------------
+
+The calling sequences are
+
+ CALL PNETU(NF,X,IPAR,RPAR,F,GMAX,IPRNT,ITERM)
+ CALL PNETS(NF,X,IX,XL,XU,IPAR,RPAR,F,GMAX,IPRNT,ITERM)
+
+The arguments have the following meaning.
+
+ Argument Type Significance
+ ----------------------------------------------------------------------
+ NF I Positive INTEGER variable that specifies the number of
+ variables of the objective function.
+ X(NF) U On input, DOUBLE PRECISION vector with the initial
+ estimate to the solution. On output, the approximation
+ to the minimum.
+ IX(NF) I On input (significant only if NB>0) INTEGER vector
+ containing the simple bounds types:
+ IX(I)=0 - the variable X(I) is unbounded,
+ IX(I)=1 - the lower bound X(I) >= XL(I),
+ IX(I)=2 - the upper bound X(I) <= XU(I),
+ IX(I)=3 - the two side bound XL(I) <= X(I) <= XU(I),
+ IX(I)=5 - the variable X(I) is fixed (given by its
+ initial estimate).
+ XL(NF) I DOUBLE PRECISION vector with lower bounds for variables
+ (significant only if NB>0).
+ XU(NF) I DOUBLE PRECISION vector with upper bounds for variables
+ (significant only if NB>0).
+ IPAR(7) I INTEGER parameters:
+ IPAR(1)=MIT, IPAR(2)=MFV, IPAR(3)=MFG,
+ IPAR(4)=IEST, IPAR(5)=MOS1, IPAR(6)=MOS2,
+ IPAR(7)=MF.
+ Parameters MIT, MFV, MFG, IEST, MOS1, MOS2, MF are
+ described in Section 3 together with other parameters
+ of the subroutine PNET.
+ RPAR(9) I DOUBLE PRECISION parameters:
+ RPAR(1)=XMAX, RPAR(2)=TOLX, RPAR(3)=TOLF,
+ RPAR(4)=TOLB, RPAR(5)=TOLG, RPAR(6)=FMIN,
+ RPAR(7)-NONE, RPAR(6)-NONE, RPAR(9)-NONE.
+ Parameters XMAX, TOLX, TOLF, TOLB, TOLG, FMIN are
+ described in Section 3 together with other parameters
+ of the subroutine PNET.
+ F O DOUBLE PRECISION value of the objective function at the
+ solution X.
+ GMAX O DOUBLE PRECISION maximum absolute value of a partial
+ derivative of the Lagrangian function.
+ IPRNT I INTEGER variable that specifies PRINT:
+ IPRNT= 0 - print is suppressed,
+ IPRNT= 1 - basic print of final results,
+ IPRNT=-1 - extended print of final results,
+ IPRNT= 2 - basic print of intermediate and final
+ results,
+ IPRNT=-2 - extended print of intermediate and final
+ results.
+ ITERM O INTEGER variable that indicates the cause of termination:
+ ITERM= 1 - if |X - XO| was less than or equal to TOLX
+ in two subsequent iterations,
+ ITERM= 2 - if |F - FO| was less than or equal to TOLF
+ in two subsequent iterations,
+ ITERM= 3 - if F is less than or equal to TOLB,
+ ITERM= 4 - if GMAX is less than or equal to TOLG,
+ ITERM= 6 - if termination criterion was not satisfied,
+ but the solution is probably acceptable,
+ ITERM=11 - if NIT exceeded MIT,
+ ITERM=12 - if NFV exceeded MFV,
+ ITERM=13 - if NFG exceeded MFG,
+ ITERM< 0 - if the method failed.
+
+ The subroutines PNETU, PNETS require the user supplied subroutines
+OBJ and DOBJ that define the objective function and its gradient and
+have the form
+
+ SUBROUTINE OBJ(NF,X,F)
+ SUBROUTINE DOBJ(NF,X,G)
+
+The arguments of the user supplied subroutines have the following
+meaning.
+
+ Argument Type Significance
+ ----------------------------------------------------------------------
+ NF I Positive INTEGER variable that specifies the number of
+ variables of the objective function.
+ X(NF) I DOUBLE PRECISION an estimate to the solution.
+ F O DOUBLE PRECISION value of the objective function at the
+ point X.
+ G(NF) O DOUBLE PRECISION gradient of the objective function
+ at the point X.
+
+
+3. Subroutine PNET:
+-------------------
+
+ This general subroutine is called from all subroutines described
+in Section 2. The calling sequence is
+
+ CALL PNET(NF,NB,X,IX,XL,XU,GF,GN,S,XO,GO,XS,GS,XM,GM,U1,U2,XMAX,
+ & TOLX,TOLF,TOLB,TOLG,FMIN,GMAX,F,MIT,MFV,MFG,IEST,MOS1,MOS2,MF,
+ & IPRNT,ITERM)
+
+
+The arguments NF, NB, X, IX, XL, XU, GMAX, F, IPRNT, ITERM, have the
+same meaning as in Section 2. Other arguments have the following meaning:
+
+ Argument Type Significance
+ -----------------------------------------------------------------------
+ GF(NF) A DOUBLE PRECISION gradient of the objective function.
+ GN(NF) A DOUBLE PRECISION old gradient of the objective function.
+ S(NF) A DOUBLE PRECISION direction vector.
+ XO(NF) A DOUBLE PRECISION array which contains increments of
+ variables.
+ GO(NF) A DOUBLE PRECISION array which contains increments of
+ gradients.
+ XS(NF) A DOUBLE PRECISION auxiliary array.
+ GS(NF) A DOUBLE PRECISION auxiliary array.
+ XM(NF*MF) A DOUBLE PRECISION array which contains increments of
+ variables.
+ GM(NF*MF) A DOUBLE PRECISION array which contains increments of
+ gradients.
+ U1(MF) A DOUBLE PRECISION auxiliary array.
+ U2(MF) A DOUBLE PRECISION auxiliary array.
+ XMAX I DOUBLE PRECISION maximum stepsize; the choice XMAX=0
+ causes that the default value 1.0D+16 will be taken.
+ TOLX I DOUBLE PRECISION tolerance for the change of the
+ coordinate vector X; the choice TOLX=0 causes that the
+ default value TOLX=1.0D-16 will be taken.
+ TOLF I DOUBLE PRECISION tolerance for the change of function
+ values; the choice TOLF=0 causes that the default
+ value TOLF=1.0D-14 will be taken.
+ TOLB I DOUBLE PRECISION minimum acceptable function value;
+ the choice TOLB=0 causes that the default value
+ TOLB=FMIN+1.0D-16 will be taken.
+ TOLG I DOUBLE PRECISION tolerance for the Lagrangian function
+ gradient; the choice TOLG=0 causes that the default
+ value TOLG=1.0D-6 will be taken.
+ FMIN I DOUBLE PRECISION lower bound for the minimum function
+ value.
+ MIT I INTEGER variable that specifies the maximum number of
+ iterations; the choice MIT=0 causes that the default
+ value 5000 will be taken.
+ MFV I INTEGER variable that specifies the maximum number of
+ function evaluations; the choice MFV=0 causes that
+ the default value 5000 will be taken.
+ MFG I INTEGER variable that specifies the maximum number of
+ gradient evaluations; the choice MFG=0 causes that
+ the default value 30000 will be taken.
+ IEST I INTEGER estimation of the minimum functiom value for
+ the line search:
+ IEST=0 - estimation is not used,
+ IEST=1 - lower bound FMIN is used as an estimation
+ for the minimum function value.
+ MOS1 I INTEGER choice of restarts after constraint change:
+ MOS1=1 - restarts are suppressed,
+ MOS1=2 - restarts with steepest descent directions are
+ used.
+ MOS2 I INTEGER choice of preconditioning strategy:
+ MOS2=1 - preconditioning is not used,
+ MOS2=2 - preconditioning by the incomplete
+ Gill-Murray decomposition,
+ MOS2=3 - preconditioning by the incomplete
+ Gill-Murray decomposition combined with
+ preliminary solution of the preconditioned
+ system.
+ MF I The number of limited-memory variable metric updates
+ in each iteration (they use 2*MF stored vectors).
+
+The choice of parameter XMAX can be sensitive in many cases. First, the
+objective function can be evaluated only in a relatively small region
+(if it contains exponentials) so that the maximum stepsize is necessary.
+Secondly, the problem can be very ill-conditioned far from the solution
+point so that large steps can be unsuitable. Finally, if the problem has
+more local solutions, a suitably chosen maximum stepsize can lead to
+obtaining a better local solution.
+ The subroutine PNET requires the user supplied subroutines OBJ
+and DOBJ which are described in Section 2.
+
+4. Verification of the subroutines:
+-----------------------------------
+
+ Subroutine PNETU can be verified and tested using the program
+TNETU. This program calls the subroutines TIUD14 (initiation), TFFU14
+(function evaluation) and TFGU14 (gradient evaluation) containing
+22 unconstrained test problems with at most 1000 variables [2]. The
+results obtained by the program TNETU on a PC computer with Microsoft
+Power Station Fortran compiler have the following form.
+
+NIT= 1481 NFV= 1656 NFG=26037 F= 0.117631766E-15 G= 0.354E-06 ITERM= 4
+NIT= 132 NFV= 387 NFG= 7945 F= 0.153382199E-15 G= 0.988E-08 ITERM= 4
+NIT= 19 NFV= 20 NFG= 110 F= 0.421204156E-09 G= 0.353E-06 ITERM= 4
+NIT= 19 NFV= 20 NFG= 230 F= 269.499543 G= 0.779E-07 ITERM= 4
+NIT= 12 NFV= 13 NFG= 49 F= 0.465606821E-11 G= 0.364E-06 ITERM= 4
+NIT= 13 NFV= 14 NFG= 76 F= 0.366783327E-11 G= 0.404E-06 ITERM= 4
+NIT= 9 NFV= 10 NFG= 37 F= 336.937181 G= 0.248E-06 ITERM= 4
+NIT= 11 NFV= 12 NFG= 58 F= 761774.954 G= 0.155E-07 ITERM= 4
+NIT= 7 NFV= 11 NFG= 28 F= 316.436141 G= 0.158E-07 ITERM= 4
+NIT= 75 NFV= 153 NFG= 3213 F= -133.610000 G= 0.777E-08 ITERM= 4
+NIT= 33 NFV= 45 NFG= 181 F= 10.7765879 G= 0.414E-07 ITERM= 4
+NIT= 23 NFV= 30 NFG= 457 F= 982.273617 G= 0.591E-08 ITERM= 4
+NIT= 7 NFV= 8 NFG= 16 F= 0.533593908E-15 G= 0.327E-07 ITERM= 4
+NIT= 1 NFV= 2 NFG= 1005 F= 0.120245125E-08 G= 0.879E-07 ITERM= 4
+NIT= 14 NFV= 15 NFG= 4033 F= 1.92401599 G= 0.468E-07 ITERM= 4
+NIT= 13 NFV= 17 NFG= 295 F= -427.404476 G= 0.800E-08 ITERM= 4
+NIT= 4 NFV= 5 NFG= 810 F=-0.379921091E-01 G= 0.537E-06 ITERM= 4
+NIT= 4 NFV= 5 NFG= 1146 F=-0.245741193E-01 G= 0.425E-06 ITERM= 4
+NIT= 10 NFV= 11 NFG= 1986 F= 59.5986241 G= 0.423E-06 ITERM= 4
+NIT= 18 NFV= 39 NFG= 3051 F= -1.00013520 G= 0.712E-07 ITERM= 4
+NIT= 7 NFV= 8 NFG= 4901 F= 2.13866377 G= 0.120E-08 ITERM= 4
+NIT= 55 NFV= 145 NFG= 4760 F= 1.00000000 G= 0.206E-08 ITERM= 4
+NITER = 1967 NFVAL = 2626 NSUCC = 22
+TIME= 0:00:06.95
+
+The rows corresponding to individual test problems contain the number of
+iterations NIT, the number of function evaluations NFV, the number of
+gradient evaluations NFG, the final value of the objective function F,
+the norm of gradient G and the cause of termination ITERM.
+ Subroutine PNETS can be verified and tested using the program
+TNETS. This program calls the subroutines TIUD14 (initiation), TFFU14
+(function evaluation), TFGU14 (gradient evaluation) containing 22 box
+constrained test problems with at most 1000 variables [2]. The results
+obtained by the program TNETS on a PC computer with Microsoft Power
+Station Fortran compiler have the following form.
+
+NIT= 1611 NFV= 1793 NFG=28524 F= 0.00000000 G= 0.000E+00 ITERM= 3
+NIT= 259 NFV= 259 NFG= 4418 F= 3930.43956 G= 0.230E-07 ITERM= 4
+NIT= 17 NFV= 18 NFG= 98 F= 0.158634811E-08 G= 0.954E-06 ITERM= 4
+NIT= 12 NFV= 13 NFG= 105 F= 269.522686 G= 0.103E-07 ITERM= 4
+NIT= 12 NFV= 13 NFG= 49 F= 0.465606821E-11 G= 0.364E-06 ITERM= 4
+NIT= 13 NFV= 14 NFG= 76 F= 0.366783327E-11 G= 0.404E-06 ITERM= 4
+NIT= 9 NFV= 10 NFG= 37 F= 336.937181 G= 0.248E-06 ITERM= 4
+NIT= 40 NFV= 41 NFG= 248 F= 761925.725 G= 0.281E-06 ITERM= 4
+NIT= 553 NFV= 555 NFG= 2056 F= 428.056916 G= 0.850E-07 ITERM= 4
+NIT= 112 NFV= 137 NFG= 2109 F= -84.1426617 G= 0.732E-06 ITERM= 4
+NIT= 7 NFV= 8 NFG= 17 F= 96517.2947 G= 0.112E-11 ITERM= 4
+NIT= 133 NFV= 136 NFG= 2689 F= 4994.21410 G= 0.180E-06 ITERM= 4
+NIT= 7 NFV= 8 NFG= 16 F= 0.533593908E-15 G= 0.327E-07 ITERM= 4
+NIT= 1 NFV= 2 NFG= 1005 F= 0.120245125E-08 G= 0.879E-07 ITERM= 4
+NIT= 14 NFV= 15 NFG= 4033 F= 1.92401599 G= 0.468E-07 ITERM= 4
+NIT= 12 NFV= 13 NFG= 294 F= -427.391653 G= 0.594E-06 ITERM= 4
+NIT= 4 NFV= 5 NFG= 810 F=-0.379921091E-01 G= 0.537E-06 ITERM= 4
+NIT= 4 NFV= 5 NFG= 1146 F=-0.245741193E-01 G= 0.425E-06 ITERM= 4
+NIT= 8 NFV= 9 NFG= 1902 F= 1654.94525 G= 0.690E-07 ITERM= 4
+NIT= 16 NFV= 25 NFG= 3254 F= -1.00013520 G= 0.836E-08 ITERM= 4
+NIT= 4 NFV= 5 NFG= 1211 F= 2.41354873 G= 0.135E-06 ITERM= 4
+NIT= 52 NFV= 137 NFG= 4843 F= 1.00000000 G= 0.657E-06 ITERM= 4
+NITER = 2900 NFVAL = 3221 NSUCC = 22
+TIME= 0:00:08.56
+
+
+References:
+-----------
+
+[1] Luksan L., Matonoha C., Vlcek J.: LSA: Algorithms for large-scale
+ unconstrained and box constrained optimization Technical Report V-896.
+ Prague, ICS AS CR, 2004.
+
+[2] Luksan L., Vlcek J.: Sparse and partially separable test problems
+ for unconstrained and equality constrained optimization. Research
+ Report V-767, Institute of Computer Science, Academy of Sciences
+ of the Czech Republic, Prague, Czech Republic, 1998.
+\1a
~ianmdlvl / nlopt.git / commitdiff