MITgcm/lsopt/lsopt_doc.txt


Description of large scale optimization package, Version 2.1.0
##############################################################
Patrick Heimbach, MIT/EAPS, 02-Mar-2000

reference:
#########

J.C. Gilbert & C. Lemarechal
Some numerical experiments with variable-storage quasi-Newton algorithms
Mathematical Programming 45 (1989), pp. 407-435

flow chart
##########

      lsopt_top
          |
          |---- check arguments
          |---- CALL INSTORE
          |       |
          |       |---- determine whether OPWARMI available:
          |                * if no:  cold start: create OPWARMI
          |                * if yes: warm start: read from OPWARMI
          |             create or open OPWARMD
          |
          |---- check consistency between OPWARMI and model parameters
          | 
          |---- >>> if COLD start: <<<
          |      |  first simulation with f.g. xx_0; output: first ff_0, gg_0
          |      |  set first preconditioner value xdiff_0 to 1
          |      |  store xx(0), gg(0), xdiff(0) to OPWARMD (first 3 entries)
          |      |
          |     >>> else: WARM start: <<<
          |         read xx(i), gg(i) from OPWARMD (first 2 entries)
          |         for first warm start after cold start, i=0
          |
          |
          |
          |---- /// if ITMAX > 0: perform optimization (increment loop index i)
          |      (
          |      )---- save current values of gg(i-1) -> gold(i-1), ff -> fold(i-1)
          |      (---- CALL LSUPDXX
          |      )       |
          |      (       |---- >>> if jmax=0 <<<
          |      )       |      |  first optimization after cold start:
          |      (       |      |  preconditioner estimated via ff_0 - ff_(first guess)
          |      )       |      |  dd(i-1) = -gg(i-1)*preco
          |      (       |      |  
          |      )       |     >>> if jmax > 0 <<<
          |      (       |         dd(i-1) = -gg(i-1)
          |      )       |         CALL HESSUPD
          |      (       |           |
          |      )       |           |---- dd(i-1) modified via Hessian approx.
          |      (       |
          |      )       |---- >>> if <dd,gg> >= 0 <<<
          |      (       |         ifail = 4
          |      )       |
          |      (       |---- compute step size: tact(i-1)
          |      )       |---- compute update: xdiff(i) = xx(i-1) + tact(i-1)*dd(i-1)
          |      (
          |      )---- >>> if ifail = 4 <<<
          |      (         goto 1000
          |      )
          |      (---- CALL OPTLINE / LSLINE
          |      )       |
          |      (       |
          |      )       |
          |      (       |---- /// loop over simulations
          |      )              (  
          |      (              )---- CALL SIMUL
          |      )              (       |
          |      (              )       |----  input: xdiff(i)
          |      )              (       |---- output: ff(i), gg(i)
          |      (              )       |---- >>> if ONLINE <<<
          |      )              (                 runs model and adjoint
          |      (              )             >>> if OFFLINE <<<
          |      )              (                 reads those values from file
          |      (              )
          |      )              (---- 1st Wolfe test:
          |      (              )     ff(i) <= tact*xpara1*<gg(i-1),dd(i-1)>
          |      )              (
          |      (              )---- 2nd Wolfe test:
          |      )              (     <gg(i),dd(i-1)> >= xpara2*<gg(i-1),dd(i-1)>
          |      (              )
          |      )              (---- >>> if 1st and 2nd Wolfe tests ok <<<
          |      (              )      |  320: update xx: xx(i) = xdiff(i)
          |      )              (      |
          |      (              )     >>> else if 1st Wolfe test not ok <<<
          |      )              (      |  500: INTERpolate new tact:
          |      (              )      |  barr*tact < tact < (1-barr)*tact
          |      )              (      |  CALL CUBIC
          |      (              )      |
          |      )              (     >>> else if 2nd Wolfe test not ok <<<
          |      (              )         350: EXTRApolate new tact:
          |      )              (         (1+barmin)*tact < tact < 10*tact
          |      (              )         CALL CUBIC
          |      )              (
          |      (              )---- >>> if new tact > tmax <<<
          |      )              (      |  ifail = 7
          |      (              )      |
          |      )              (---- >>> if new tact < tmin OR tact*dd < machine precision <<<
          |      (              )      |  ifail = 8
          |      )              (      |
          |      (              )---- >>> else <<<
          |      )              (         update xdiff for new simulation
          |      (              )
          |      )             \\\ if nfunc > 1: use inter-/extrapolated tact and xdiff
          |      (                               for new simulation
          |      )                               N.B.: new xx is thus not based on new gg, but
          |      (                                     rather on new step size tact
          |      )        
          |      (        
          |      )        
          |      (---- store new values xx(i), gg(i) to OPWARMD (first 2 entries)
          |      )---- >>> if ifail = 7,8,9 <<<
          |      (         goto 1000
          |      )
          |      (---- compute new pointers jmin, jmax to include latest values
          |      )     gg(i)-gg(i-1), xx(i)-xx(i-1) to Hessian matrix estimate
          |      (---- store gg(i)-gg(i-1), xx(i)-xx(i-1) to OPWARMD
          |      )     (entries 2*jmax+2, 2*jmax+3)
          |      (
          |      )---- CALL DGSCALE
          |      (       |
          |      )       |---- call dostore
          |      (       |       |
          |      )       |       |---- read preconditioner of previous iteration diag(i-1)
          |      (       |             from OPWARMD (3rd entry)
          |      )       |
          |      (       |---- compute new preconditioner diag(i), based upon diag(i-1),
          |      )       |     gg(i)-gg(i-1), xx(i)-xx(i-1)
          |      (       |
          |      )       |---- call dostore
          |      (               |
          |      )               |---- write new preconditioner diag(i) to OPWARMD (3rd entry)
          |      (
          |---- \\\ end of optimization iteration loop
          |
          |
          |
          |---- CALL OUTSTORE
          |       |
          |       |---- store gnorm0, ff(i), current pointers jmin, jmax, iterabs to OPWARMI
          |
          |---- >>> if OFFLINE version <<<
          |         xx(i+1) needs to be computed as input for offline optimization
          |          |
          |          |---- CALL LSUPDXX
          |          |       |
          |          |       |---- compute dd(i), tact(i) -> xdiff(i+1) = x(i) + tact(i)*dd(i)
          |          |
          |          |---- CALL WRITE_CONTROL
          |          |       |
          |          |       |---- write xdiff(i+1) to special file for offline optim.
          |
          |---- print final information
          |
          O


Remarks:
#######

1. Difference between offline/online version
--------------------------------------------

- Offline version: Every call to simul refers to a read procedure which
                   reads the result of an offline forward and adjoint run
                   Therefore, only one call to simul is allowed,
                     itmax = 0, for cold start
                     itmax = 1, for warm start
                   Also, at the end, x(i+1) needs to be computed and saved
                   to be available for the offline model and adjoint run

-  Online version: Every call to simul refers to an execution of the forward and adjoint model.
                   Several iterations of optimization may thus be performed within
                   a single run of the main program (main_lsopt).
                   The following cases may occur:
                     - cold start only (no optimization)
                     - cold start & one or several iterations of optimization
                     - warm start from previous cold start with one or several iterations
                     - warm start from previous warm start with one or several iterations

In order to achieve minimum difference between the online and offline code
xdiff(i+1) is stored to file at the end of an (offline) iteration,
but recomputed identically at the beginning of the next iteration.

2. Number of iterations vs. number of simulations
-------------------------------------------------

- itmax: controls the max. number of iterations
- nfunc: controls the max. number of simulations within one iteration

Summary: From one iteration to the next the descent direction changes.
         Within one iteration more than one forward and adjoint run may be performed.
         The updated control used as input for these simulations uses the same
         descent direction, but different step sizes.

In detail:
From one iteration to the next the descent direction dd changes using
the result for the adjoint vector gg of the previous iteration.
In lsline the updated control xdiff(i,1) = xx(i-1) + tact(i-1,1)*dd(i-1) serves as input for
a forward and adjoint model run yielding a new gg(i,1).
In general, the new solution passes the 1st and 2nd Wolfe tests 
so xdiff(i,1) represents the solution sought: xx(i) = xdiff(i,1).
If one of the two tests fails, an inter- or extrapolation is invoked to determine
a new step size tact(i-1,2).
If more than one function call is permitted, the new step size is used together
with the "old" descent direction dd(i-1) (i.e. dd is not updated using the new gg(i)),
to compute a new xdiff(i,2) = xx(i-1) + tact(i-1,2)*dd(i-1) that serves as input
in a new forward and adjoint run, yielding gg(i,2).
If now, both Wolfe tests are successfull, the updated solution is given by
xx(i) = xdiff(i,2) = xx(i-1) + tact(i-1,2)*dd(i-1).

3. Double-usage of fields dd and xdiff
--------------------------------------

In order to save memory both the fields dd and xdiff have a double usage.

- xdiff: in lsopt_top: used as x(i) - x(i-1) for Hessian update
         in lsline:    intermediate result for control update x = x + tact*dd

- dd   : in lsopt_top, lsline: descent vector, dd = -gg   & hessupd
         in dgscale:           intermediate result to compute new preconditioner

4. Notice for user of old code
------------------------------

Three relevant changes needed to switch to new version:
  
  (i): OPWARMI file: two variables added:
               gnorm0  : norm of first (cold start) gradient
               iabsiter: total number of iterations with respect to cold start

 (ii): routine names that are referenced by main_lsopt.f
       lsoptv1 -> lsopt_top
       lsline1 -> lsline

(iii): parameter list of lsopt_top
       logical loffline included

parameter file lsopt.par
########################

The optimization is controlled by a set of parameters
provided through the standard input file lsopt.par,
which is generated within the job script.

  NUPDATE  : max. no. of update pairs (gg(i)-gg(i-1), xx(i)-xx(i-1))
             to be stored in OPWARMD to estimate Hessian
             [pair of current iter. is stored in (2*jmax+2, 2*jmax+3)
             jmax must be > 0 to access these entries]
             Presently NUPDATE must be > 0 
             (i.e. iteration without reference to previous
              iterations through OPWARMD has not been tested)
  EPSX     : relative precision on xx bellow which xx should not be improved
  EPSG     : relative precision on gg below which optimization is considered successful
  IPRINT   : controls verbose (>=1) or non-verbose output
  NUMITER  : max. number of iterations of optimisation
             NUMTER = 0: cold start only, no optimization
  ITER_NUM : index of new restart file to be created (not necessarily = NUMITER!)
  NFUNC    : max. no. of simulations per iteration
             (must be > 0)
             is used if step size tact is inter-/extrapolated;
             in this case, if NFUNC > 1, a new simulation is performed with
             same gradient but "improved" step size
  FMIN     : first guess cost function value
             (only used as long as first iteration not completed,
             i.e. for jmax <= 0)

OPWARMI, OPWARMD files
######################

Two files retain values of previous iterations which are
used in latest iteration to update Hessian.
OPWARMI: contains index settings and scalar variables
OPWARMD: contains vectors

Structure of OPWARMI file:
-------------------------
   
    n, fc, isize, m, jmin, jmax, gnorm0, iabsiter

    n  = nn      : no. of control variables
    fc = ff      : cost value of last iteration
    isize        : no. of bytes per record in OPWARMD
    m = nupdate  : max. no. of updates for Hessian
    jmin, jmax   : pointer indices for OPWARMD file (cf. below)
    gnorm0       : norm of first (cold start) gradient gg
    iabsiter     : total number of iterations with respect to cold start

Structure of OPWARMD file:
-------------------------
   entry
     1    : xx(i)         : control vector of latest iteration
     2    : gg(i)         : gradient of latest iteration
     3    : xdiff(i), diag: preconditioning vector; (1,...,1) for cold start
    ---
 2*jmax+2 : gold = g(i) - g(i-1) for last update (jmax)
 2*jmax+3 : xdiff = tact * d = xx(i) - xx(i-1) for last update (jmax)

if jmax = 0: cold start; no Hessian update used to compute dd
if jmax > nupdate, old positions are overwritten, starting
                with position pair (4,5)

Example 1: jmin = 1, jmax = 3, mupd = 5

  1   2   3   |   4   5     6   7     8   9     empty     empty
|___|___|___| | |___|___| |___|___| |___|___| |___|___| |___|___|
      0       |     1         2         3

Example 2: jmin = 3, jmax = 7, mupd = 5   ---> jmax = 2

  1   2   3   |  
|___|___|___| | |___|___| |___|___| |___|___| |___|___| |___|___|
              |     6         7         3         4         5


Error handling
##############

  ifail |   description
--------+----------------------------------------------------------
   < 0  | should not appear (flag indic in simul.F not used)
     0  | normal mode during execution
     1  | an input argument is wrong
     2  | warm start file is corrupted
     3  | the initial gradient is too small
     4  | the search direction is not a descent one
     5  | maximal number of iterations reached
     6  | maximal number of simulations reached (handled passively)
     7  | the linesearch failed
     8  | the function could not be improved
     9  | optline parameters wrong
    10  | cold start, no optimization done
    11  | convergence achieved within precision


1
2	Description of large scale optimization package, Version 2.1.0
3	##############################################################
4	Patrick Heimbach, MIT/EAPS, 02-Mar-2000
5
6	reference:
7	#########
8
9	J.C. Gilbert & C. Lemarechal
10	Some numerical experiments with variable-storage quasi-Newton algorithms
11	Mathematical Programming 45 (1989), pp. 407-435
12
13	flow chart
14	##########
15
16	lsopt_top
17	\|
18	\|---- check arguments
19	\|---- CALL INSTORE
20	\| \|
21	\| \|---- determine whether OPWARMI available:
22	\| * if no: cold start: create OPWARMI
23	\| * if yes: warm start: read from OPWARMI
24	\| create or open OPWARMD
25	\|
26	\|---- check consistency between OPWARMI and model parameters
27	\|
28	\|---- >>> if COLD start: <<<
29	\| \| first simulation with f.g. xx_0; output: first ff_0, gg_0
30	\| \| set first preconditioner value xdiff_0 to 1
31	\| \| store xx(0), gg(0), xdiff(0) to OPWARMD (first 3 entries)
32	\| \|
33	\| >>> else: WARM start: <<<
34	\| read xx(i), gg(i) from OPWARMD (first 2 entries)
35	\| for first warm start after cold start, i=0
36	\|
37	\|
38	\|
39	\|---- /// if ITMAX > 0: perform optimization (increment loop index i)
40	\| (
41	\| )---- save current values of gg(i-1) -> gold(i-1), ff -> fold(i-1)
42	\| (---- CALL LSUPDXX
43	\| ) \|
44	\| ( \|---- >>> if jmax=0 <<<
45	\| ) \| \| first optimization after cold start:
46	\| ( \| \| preconditioner estimated via ff_0 - ff_(first guess)
47	\| ) \| \| dd(i-1) = -gg(i-1)*preco
48	\| ( \| \|
49	\| ) \| >>> if jmax > 0 <<<
50	\| ( \| dd(i-1) = -gg(i-1)
51	\| ) \| CALL HESSUPD
52	\| ( \| \|
53	\| ) \| \|---- dd(i-1) modified via Hessian approx.
54	\| ( \|
55	\| ) \|---- >>> if <dd,gg> >= 0 <<<
56	\| ( \| ifail = 4
57	\| ) \|
58	\| ( \|---- compute step size: tact(i-1)
59	\| ) \|---- compute update: xdiff(i) = xx(i-1) + tact(i-1)*dd(i-1)
60	\| (
61	\| )---- >>> if ifail = 4 <<<
62	\| ( goto 1000
63	\| )
64	\| (---- CALL OPTLINE / LSLINE
65	\| ) \|
66	\| ( \|
67	\| ) \|
68	\| ( \|---- /// loop over simulations
69	\| ) (
70	\| ( )---- CALL SIMUL
71	\| ) ( \|
72	\| ( ) \|---- input: xdiff(i)
73	\| ) ( \|---- output: ff(i), gg(i)
74	\| ( ) \|---- >>> if ONLINE <<<
75	\| ) ( runs model and adjoint
76	\| ( ) >>> if OFFLINE <<<
77	\| ) ( reads those values from file
78	\| ( )
79	\| ) (---- 1st Wolfe test:
80	\| ( ) ff(i) <= tactxpara1<gg(i-1),dd(i-1)>
81	\| ) (
82	\| ( )---- 2nd Wolfe test:
83	\| ) ( <gg(i),dd(i-1)> >= xpara2*<gg(i-1),dd(i-1)>
84	\| ( )
85	\| ) (---- >>> if 1st and 2nd Wolfe tests ok <<<
86	\| ( ) \| 320: update xx: xx(i) = xdiff(i)
87	\| ) ( \|
88	\| ( ) >>> else if 1st Wolfe test not ok <<<
89	\| ) ( \| 500: INTERpolate new tact:
90	\| ( ) \| barrtact < tact < (1-barr)tact
91	\| ) ( \| CALL CUBIC
92	\| ( ) \|
93	\| ) ( >>> else if 2nd Wolfe test not ok <<<
94	\| ( ) 350: EXTRApolate new tact:
95	\| ) ( (1+barmin)tact < tact < 10tact
96	\| ( ) CALL CUBIC
97	\| ) (
98	\| ( )---- >>> if new tact > tmax <<<
99	\| ) ( \| ifail = 7
100	\| ( ) \|
101	\| ) (---- >>> if new tact < tmin OR tact*dd < machine precision <<<
102	\| ( ) \| ifail = 8
103	\| ) ( \|
104	\| ( )---- >>> else <<<
105	\| ) ( update xdiff for new simulation
106	\| ( )
107	\| ) \\\ if nfunc > 1: use inter-/extrapolated tact and xdiff
108	\| ( for new simulation
109	\| ) N.B.: new xx is thus not based on new gg, but
110	\| ( rather on new step size tact
111	\| )
112	\| (
113	\| )
114	\| (---- store new values xx(i), gg(i) to OPWARMD (first 2 entries)
115	\| )---- >>> if ifail = 7,8,9 <<<
116	\| ( goto 1000
117	\| )
118	\| (---- compute new pointers jmin, jmax to include latest values
119	\| ) gg(i)-gg(i-1), xx(i)-xx(i-1) to Hessian matrix estimate
120	\| (---- store gg(i)-gg(i-1), xx(i)-xx(i-1) to OPWARMD
121	\| ) (entries 2jmax+2, 2jmax+3)
122	\| (
123	\| )---- CALL DGSCALE
124	\| ( \|
125	\| ) \|---- call dostore
126	\| ( \| \|
127	\| ) \| \|---- read preconditioner of previous iteration diag(i-1)
128	\| ( \| from OPWARMD (3rd entry)
129	\| ) \|
130	\| ( \|---- compute new preconditioner diag(i), based upon diag(i-1),
131	\| ) \| gg(i)-gg(i-1), xx(i)-xx(i-1)
132	\| ( \|
133	\| ) \|---- call dostore
134	\| ( \|
135	\| ) \|---- write new preconditioner diag(i) to OPWARMD (3rd entry)
136	\| (
137	\|---- \\\ end of optimization iteration loop
138	\|
139	\|
140	\|
141	\|---- CALL OUTSTORE
142	\| \|
143	\| \|---- store gnorm0, ff(i), current pointers jmin, jmax, iterabs to OPWARMI
144	\|
145	\|---- >>> if OFFLINE version <<<
146	\| xx(i+1) needs to be computed as input for offline optimization
147	\| \|
148	\| \|---- CALL LSUPDXX
149	\| \| \|
150	\| \| \|---- compute dd(i), tact(i) -> xdiff(i+1) = x(i) + tact(i)*dd(i)
151	\| \|
152	\| \|---- CALL WRITE_CONTROL
153	\| \| \|
154	\| \| \|---- write xdiff(i+1) to special file for offline optim.
155	\|
156	\|---- print final information
157	\|
158	O
159
160
161
162	Remarks:
163	#######
164
165	1. Difference between offline/online version
166	--------------------------------------------
167
168	- Offline version: Every call to simul refers to a read procedure which
169	reads the result of an offline forward and adjoint run
170	Therefore, only one call to simul is allowed,
171	itmax = 0, for cold start
172	itmax = 1, for warm start
173	Also, at the end, x(i+1) needs to be computed and saved
174	to be available for the offline model and adjoint run
175
176	- Online version: Every call to simul refers to an execution of the forward and adjoint model.
177	Several iterations of optimization may thus be performed within
178	a single run of the main program (main_lsopt).
179	The following cases may occur:
180	- cold start only (no optimization)
181	- cold start & one or several iterations of optimization
182	- warm start from previous cold start with one or several iterations
183	- warm start from previous warm start with one or several iterations
184
185	In order to achieve minimum difference between the online and offline code
186	xdiff(i+1) is stored to file at the end of an (offline) iteration,
187	but recomputed identically at the beginning of the next iteration.
188
189	2. Number of iterations vs. number of simulations
190	-------------------------------------------------
191
192	- itmax: controls the max. number of iterations
193	- nfunc: controls the max. number of simulations within one iteration
194
195	Summary: From one iteration to the next the descent direction changes.
196	Within one iteration more than one forward and adjoint run may be performed.
197	The updated control used as input for these simulations uses the same
198	descent direction, but different step sizes.
199
200	In detail:
201	From one iteration to the next the descent direction dd changes using
202	the result for the adjoint vector gg of the previous iteration.
203	In lsline the updated control xdiff(i,1) = xx(i-1) + tact(i-1,1)*dd(i-1) serves as input for
204	a forward and adjoint model run yielding a new gg(i,1).
205	In general, the new solution passes the 1st and 2nd Wolfe tests
206	so xdiff(i,1) represents the solution sought: xx(i) = xdiff(i,1).
207	If one of the two tests fails, an inter- or extrapolation is invoked to determine
208	a new step size tact(i-1,2).
209	If more than one function call is permitted, the new step size is used together
210	with the "old" descent direction dd(i-1) (i.e. dd is not updated using the new gg(i)),
211	to compute a new xdiff(i,2) = xx(i-1) + tact(i-1,2)*dd(i-1) that serves as input
212	in a new forward and adjoint run, yielding gg(i,2).
213	If now, both Wolfe tests are successfull, the updated solution is given by
214	xx(i) = xdiff(i,2) = xx(i-1) + tact(i-1,2)*dd(i-1).
215
216	3. Double-usage of fields dd and xdiff
217	--------------------------------------
218
219	In order to save memory both the fields dd and xdiff have a double usage.
220
221	- xdiff: in lsopt_top: used as x(i) - x(i-1) for Hessian update
222	in lsline: intermediate result for control update x = x + tact*dd
223
224	- dd : in lsopt_top, lsline: descent vector, dd = -gg & hessupd
225	in dgscale: intermediate result to compute new preconditioner
226
227	4. Notice for user of old code
228	------------------------------
229
230	Three relevant changes needed to switch to new version:
231
232	(i): OPWARMI file: two variables added:
233	gnorm0 : norm of first (cold start) gradient
234	iabsiter: total number of iterations with respect to cold start
235
236	(ii): routine names that are referenced by main_lsopt.f
237	lsoptv1 -> lsopt_top
238	lsline1 -> lsline
239
240	(iii): parameter list of lsopt_top
241	logical loffline included
242
243	parameter file lsopt.par
244	########################
245
246	The optimization is controlled by a set of parameters
247	provided through the standard input file lsopt.par,
248	which is generated within the job script.
249
250	NUPDATE : max. no. of update pairs (gg(i)-gg(i-1), xx(i)-xx(i-1))
251	to be stored in OPWARMD to estimate Hessian
252	[pair of current iter. is stored in (2jmax+2, 2jmax+3)
253	jmax must be > 0 to access these entries]
254	Presently NUPDATE must be > 0
255	(i.e. iteration without reference to previous
256	iterations through OPWARMD has not been tested)
257	EPSX : relative precision on xx bellow which xx should not be improved
258	EPSG : relative precision on gg below which optimization is considered successful
259	IPRINT : controls verbose (>=1) or non-verbose output
260	NUMITER : max. number of iterations of optimisation
261	NUMTER = 0: cold start only, no optimization
262	ITER_NUM : index of new restart file to be created (not necessarily = NUMITER!)
263	NFUNC : max. no. of simulations per iteration
264	(must be > 0)
265	is used if step size tact is inter-/extrapolated;
266	in this case, if NFUNC > 1, a new simulation is performed with
267	same gradient but "improved" step size
268	FMIN : first guess cost function value
269	(only used as long as first iteration not completed,
270	i.e. for jmax <= 0)
271
272	OPWARMI, OPWARMD files
273	######################
274
275	Two files retain values of previous iterations which are
276	used in latest iteration to update Hessian.
277	OPWARMI: contains index settings and scalar variables
278	OPWARMD: contains vectors
279
280	Structure of OPWARMI file:
281	-------------------------
282
283	n, fc, isize, m, jmin, jmax, gnorm0, iabsiter
284
285	n = nn : no. of control variables
286	fc = ff : cost value of last iteration
287	isize : no. of bytes per record in OPWARMD
288	m = nupdate : max. no. of updates for Hessian
289	jmin, jmax : pointer indices for OPWARMD file (cf. below)
290	gnorm0 : norm of first (cold start) gradient gg
291	iabsiter : total number of iterations with respect to cold start
292
293	Structure of OPWARMD file:
294	-------------------------
295	entry
296	1 : xx(i) : control vector of latest iteration
297	2 : gg(i) : gradient of latest iteration
298	3 : xdiff(i), diag: preconditioning vector; (1,...,1) for cold start
299	---
300	2*jmax+2 : gold = g(i) - g(i-1) for last update (jmax)
301	2jmax+3 : xdiff = tact d = xx(i) - xx(i-1) for last update (jmax)
302
303	if jmax = 0: cold start; no Hessian update used to compute dd
304	if jmax > nupdate, old positions are overwritten, starting
305	with position pair (4,5)
306
307	Example 1: jmin = 1, jmax = 3, mupd = 5
308
309	1 2 3 \| 4 5 6 7 8 9 empty empty
310	\|___\|___\|___\| \| \|___\|___\| \|___\|___\| \|___\|___\| \|___\|___\| \|___\|___\|
311	0 \| 1 2 3
312
313	Example 2: jmin = 3, jmax = 7, mupd = 5 ---> jmax = 2
314
315	1 2 3 \|
316	\|___\|___\|___\| \| \|___\|___\| \|___\|___\| \|___\|___\| \|___\|___\| \|___\|___\|
317	\| 6 7 3 4 5
318
319
320
321	Error handling
322	##############
323
324	ifail \| description
325	--------+----------------------------------------------------------
326	< 0 \| should not appear (flag indic in simul.F not used)
327	0 \| normal mode during execution
328	1 \| an input argument is wrong
329	2 \| warm start file is corrupted
330	3 \| the initial gradient is too small
331	4 \| the search direction is not a descent one
332	5 \| maximal number of iterations reached
333	6 \| maximal number of simulations reached (handled passively)
334	7 \| the linesearch failed
335	8 \| the function could not be improved
336	9 \| optline parameters wrong
337	10 \| cold start, no optimization done
338	11 \| convergence achieved within precision
339
340