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$$$$ EXCE     NOTICE  CHAT      11/09/12    21:16:06     7124           
                                             DATE     11/09/12

  Operateur EXCELLENCE                     Voir aussi :
    --------------------   
    TAB1 = EXCE  TAB1 ;
                                    TAB1.'VX0'   .'VF'    .'VXMIN'
                                        .'VXMAX' .'MC'    .'VCMAX'
                                        .'METHODE'        .'DELTA0'
                                        .'MAXITERATION'   .'XSMAX'
                                        .'VDIS'   .'T0'   .'S0'
                                        


    Description :
    -------------

    The EXCELL operator computes the minimum of a function F(Xi),the used 
method is the well-known MMA (Method of Moving Asymptotes) proposed 
by K.Svanberg. The purpose is to find the minimum of a function F(Xi)
with i=1,N given that :

   - the relations Cj(Xi) < Cjmax (j>0 and j=1,M) must be satisfied

   - there are relations on each unknown  Ximin <  Xi < Ximax

    The functions F and Cj are defined by the function values and 
 by their derivatives at the starting point X0.



    Input data :
    ------------

 TAB1.'VX0'        : table (VECTEUR subtype) containing the
                     variables initial values X0i.
                     The table indices are integers i (i=1,N)

 TAB1.'VF'         : table (VECTEUR subtype) in which :
                   - TAB1.'VF'.0 : is the value of F(X0)
                   - TAB1.'VF'.I : is the value of the derivative
                     of F with respect to Xi at X0 (i=1,N)

 TAB1.'MC'         : table indexed by integers j (j=1,M) containing 
                     as many tables as there are relations Cj

      TAB1.'MC'.J    is a table which stands for the function Cj 
                     in which :
                    - TAB1.'MC'.J.0 : is the initial value of Cj(X0)
                    - TAB1.'MC'.J.I : is the value of the derivative
                      of Cj with respect to Xi at X0 (i=1,N).

 TAB1.'VXMIN'      : table (VECTEUR subtype) indexed by integers
                     in which :
                    - TAB1.'VXMIN'.I : is the value of Ximin

 TAB1.'VXMAX'      : table (VECTEUR subtype) indexed by integers
                     in which :             
                    - TAB1.'VXMAX'.I : is the value of Ximax

 TAB1.'VCMAX'      : table (VECTEUR subtype) indexed by integers
                     in which :  
                    - TAB1.'VCMAX'.J : is the value of Cjmax

 TAB1.'METHODE'    : (optional) is a MOT(word) specifying the method
                     of linearization to be used

                    - 'STA' for using the standard method
                    - 'MOV' if the functions are "strongly" non-linear 
                    - 'LIN' if the functions are rather linear
                      and if there are discrete variables
                       
 TAB1.'T0'         :  (optional) changes the value of the real number
                      ranging between 0. and 1. which governs the convexity
                      of the functions. The greater t0, the convexer
                      the functions. By default, for the standard
                      method, t0 is considered to equal 0.3333 

 TAB1.'S0'         : (optional) changes the value of the real number
                      ranging between 0. and 1. which governs the convexity
                      of the functions. The greater s0, the convexer
                      the functions. By default, for the 'MOV' method, 
                      s0 is considered to equal 0.7 

 TAB1.'MAXITERATION' : (optional) changes the maximum value 
                       permitted for the number of iterations.
                       (By default 100)

 TAB1.'VDIS'       : table indexed by integers k (k=1,KK) 
                     containing as many tables as there are variables
                     with permitted discrete values. This option 
                     is not yet available.

    Note :
    --------      -  at first the variables X0i must satisfy the 
                     following conditions   Ximin < X0i < Ximax

                  -  the relations Cj < Cjmax are not necessarily
                     satisfied at the starting point X0. In this case,
                     a new relaxation variable is input but the
                     solution found by EXCELL may still not satisfy 
                     the relations either.
                     The effect of this relaxation variable can
                     be modified by two real numbers TAB1.'DELTA0' 
                     and TAB1.'XSMAX'. By default
                     DELTA0=50. and XSMAX=500.
                    ( DELTA0 > 1. and XSMAX > DELTA0 are requested)

    Example :
    ---------

    The function which the user wishes to minimize is not that
 minimized by the EXCE operator. First, he must solve a few
 problems. From a known state of variables, EXCE is asked to compute 
 the minimum of an approximate problem, the function F to be minimized
 is replaced with the linearized function described above as well
 as the functions C. Then one starts again from the solution found 
 by EXCE. The algorithm is as follows :

       - creation of TABLES objects.
       - initialization of TAB1.'VX0' (values of Xi0)
       - initialization of TAB1.'VF'.
       - initialization of TAB1.'MC'.  J .
       - initialization of TAB1.'VXMIN' and TAB1.'VXMAX'
       - initialization of TAB1.'VCMAX'
       - repeat 5 times  :
          - computation of DF and set in TAB1.'VF', as well as F(XI0)
          - computation of Cj and set in  TAB1.'MC'.j.
            as well as Cj(Xi0)
          - call on EXCE with TAB1 on input.
          - print TAB1.'VX0'
       - loop end