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C  Global Variables and Recursive Calls

The use of globally defined variables in TOMLAB  is well motivated, for example to avoid unnecessary evaluations, storage of sparse patterns, internal communication, computation of elapsed CPU time etc. The global variables used in TOMLAB  are listed in Table 30 and 31.

Even though global variables is efficient to use in many cases, it will be trouble with recursive algorithms and recursive calls. Therefore, the routines globalSave  and globalGet  have been defined. The globalSave  routine saves all global variables in a structure glbSave(depth)  and then initialize all of them as empty. By using the depth variable, an arbitrarily number of recursions are possible. The other routine globalGet  retrieves all global variables in the structure glbSave(depth) .

For solving some kinds of problems it could be suitable or even necessary to apply algorithms which is based on a recursive approach. A common case occurs when an optimization solver calls another solver to solve a subproblem. For example, the EGO algorithm (implemented in the routine ego ) solves an unconstrained (uc) and a box-bounded global optimization problem (glb) in each iteration. To avoid that the global variables are not re-initialized or given new values by the underlying procedure TOMLAB  saves the global variables in the workspace before the underlying procedure is called. Directly after the call to the underlying procedure the global variables are restored.

To illustrate the idea, the following code would be a possible part of the ego  code, where the routines globalSave  and globalGet  are called.

...
...
   global GlobalLevel
   if isempty(GlobalLevel)
      GlobalLevel=1;
   else
      GlobalLevel=GlobalLevel+1;
   end
   Level=GlobalLevel
   globalSave(Level);

   EGOResult = glbSolve(EGOProb);

   globalGet(Level);
   GlobalLevel=GlobalLevel-1;
...
...
   Level=GlobalLevel
   globalSave(Level);

   [DACEResult] = ucSolve(DACEProb);

   globalGet(1);
   globalGet(Level);
   GlobalLevel=GlobalLevel-1;
...
...

In most cases the user does not need to define the above statements and instead use the special driver routine tomSolve  that does the above global variable checks and savings and calls the solver in between. In the actual implementation of the ego  solver the above code is simplified to the following:

...
...
   EGOResult = tomSolve('glbSolve',EGOProb);
...
...
   DACEResult = tomSolve('ucSolve',DACEProb);
...
...

This safely handles the global variables and is the recommended way for users in need of recursive optimization solutions.

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Table 30: The global variables used in TOMLAB 

Name	Description
MAXCOLS	Number of screen columns. Default 120.
MAXMENU	Number of menu items showed on one screen. Default 50.
MAX_c	Maximum number of constraints to be printed.
MAX_x	Maximum number of variables to be printed.
MAX_r	Maximum number of residuals to be printed.
CUTEPATH	The path ending with \cute.
CUTEDLL	Name of CUTE DLL file.
DLLPATH	Full path to the CUTE DLL file.
CUTE_g	Gradient.
CUTE_H	Hessian.
CUTE_Hx	Value of x  when computing CUTE_H .
CUTE_dc	Constraint normals.
CUTE_Equal	Binary vector, element i equals 1 if constraint i is an equality constraint.
CUTE_Linear	Binary vector, element i equals 1 if constraint i is a linear constraint.
n_f	Counter for the number of function evaluations.
n_g	Counter for the number of gradient evaluations.
n_H	Counter for the number of Hessian evaluations.
n_c	Counter for the number of constraint evaluations.
n_dc	Counter for the number of constraint normal evaluations.
n_d2c	Counter for the number of evaluations of the 2nd part of 2nd derivative matrix of the Lagrangian function.
n_r	Counter for the number of residual evaluations.
n_J	Counter for the number of Jacobian evaluations.
n_d2r	Counter for the number of evaluations of the 2nd part of the Hessian for a nonlinear least squares problem .
NLP_x	Value of x  when computing NLP_f .
NLP_f	Function value.
NLP_xg	Value of x  when computing NLP_g .
NLP_g	Gradient value.
NLP_xH	Value of x  when computing NLP_H .
NLP_H	Hessian value.
NLP_xc	Value of x  when computing NLP_c .
NLP_c	Constraints value.
NLP_pSepFunc	Number of partially separable functions.
NLP_pSepIndex	Index for the separated function computed.

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Table 31: The global variables used in TOMLAB 

Name	Description
US_A	Problem dependent information sent between user routines. The user is recommended to always use this variable.
LS_A	Problem dependent information sent from residual routine to Jacobian routine.
LS_x	Value of x  when computing LS_r
LS_r	Residual value.
LS_xJ	Value of x  when computing LS_J
LS_J	Jacobian value.
SEP_z	Separated variables z .
SEP_Jz	Jacobian for separated variables z .
wNLLS	Weighting of least squares residuals (internal variable in nlp_r  and nlp_J ).
alphaV	Vector with all step lengths α for each iteration.
BUILDP	Flag.
F_X	Matrix with function values.
pLen	Number of iterations so far.
p_dx	Matrix with all search directions.
X_max	The biggest x-values for all iterations.
X_min	The smallest x-values for all iterations.
X_NEW	Last x point in line search. Possible new x_k.
X_OLD	Last known base point xk
probType	Defines the type of optimization problem.
solvType	Defines the solver type.
answer	Used by the GUI for user control options.
instruction	Used by the GUI for user control options.
question	Used by the GUI for user control options.
plotData	Structure with plotting parameters.
Prob	Problem structure, see Table A.
Result	Result structure, see Table B.
runNumber	Vector index when Result  is an array of structures.
TIME0	Used to compute CPU time and real time elapsed.
TIME1	Used to compute CPU time and real time elapsed
cJPI	Used to store sparsity pattern for the constraint Jacobian when automatic differentiation is used.
HPI	Used to store sparsity pattern for the Hessian when automatic differentiation is used.
JPI	Used to store sparsity pattern for the Jacobian when automatic differentiation is used.
glbSave	Used to save global variables in recursive calls to TOMLAB.

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