22 - LINEARLY CONSTRAINED MINIMAX MINIMIZATION
----------------------------------------------


      CALL EIUD22(N,NA,NAL,NC,NCL,X,IX,XL,XU,IC,CL,CU,CG,
     &            FMIN,XMAX,NEXT,IEXT,IERR)

         N - NUMBER OF VARIABLES (INPUT-DECLARED, OUTPUT-ACTUAL)
         NA - NUMBER OF FUNCTIONS IN THE SUM OF SQUARES
                (INPUT-DECLARED, OUTPUT-ACTUAL)
         NAL - NUMBER OF LINEAR FUNCTIONS IN THE SUM OF SQUARES
                (OUTPUT - ALWAYS ZERO)
         NC - NUMBER OF GENERAL CONSTRAINTS (OUTPUT)
         NCL - NUMBER OF LINEAR CONSTRAINTS (OUTPUT - ALWAYS NC)
         X(N) - INITIAL VECTOR OF VARIABLES (OUTPUT)
         IX(N) - TYPES OF SIMPLE BOUNDS (OUTPUT):
                IX(I)=0 FOR UNBOUNDED VARIABLE,
                IX(I)=1 FOR LOWER BOUND XL(I) <= X(I),
                IX(I)=2 FOR UPPER BOUND X(I) <= XU(I),
                IX(I)=3 FOR TWO SIDED BOUND XL(I) <= X(I) <= XU(I)
         XL(N) - VECTOR OF LOWER BOUNDS (OUTPUT)
         XU(N) - VECTOR OF UPPER BOUNDS (OUTPUT)
         IC(NC) - TYPES OF GENERAL CONSTRAINTS (OUTPUT):
                IC(KC)=1 FOR LOWER CONSTRAINT CL(KC) <= FC(KC),
                IC(KC)=2 FOR UPPER CONSTRAINT FC(KC) <= CU(KC),
                IC(KC)=3 FOR TWO SIDED CONSTRAINT
                CL(KC) <= FC(KC) <= CU(KC)
         CL(NC) - VECTOR OF LOWER CONSTRAINTS (OUTPUT)
         CU(NC) - VECTOR OF UPPER CONSTRAINTS (OUTPUT)
         CG(NC*N) - COEFFICIENTS OF LINEAR CONSTRAINTS (OUTPUT)
         FMIN - LOWER BOUND OF OBJECTIVE FUNCTION (OUTPUT)
         XMAX - UPPER BOUND OF STEPSIZE (OUTPUT)
         NEXT - NO. OF PROBLEM (INPUT): THERE ARE 15 PROBLEMS
                (NEXT FROM 1 TO 15)
         IEXT - TYPE OF EXTREMUM
                (IEXT<0-MAXIMIN, IEXT=0-CHEBYSHEV NORM, IEXT=1-MINIMAX)
         IERR - CONFLICT IN INPUT DATA IF IERR <> 0 (OUTPUT)


      CALL EAFU22(N,KA,X,FA,NEXT)

         N - NUMBER OF VARIABLES (INPUT)
         KA - INDEX OF THE GIVEN FUNCTION IN THE SUM OF SQUARES (INPUT)
         X(N) - ACTUAL VECTOR OF VARIABLES (INPUT)
         FA - VALUE OF THE GIVEN FUNCTION WITH THE INDEX KA (OUTPUT)
         NEXT - NO. OF PROBLEM (INPUT)


      CALL EAGU22(N,KA,X,GA,NEXT)

         N - NUMBER OF VARIABLES (INPUT)
         KA - INDEX OF THE GIVEN FUNCTION IN THE SUM OF SQUARES (INPUT)
         X(N) - ACTUAL VECTOR OF VARIABLES (INPUT)
         GA(N) - GRADIENT OF THE GIVEN FUNCTION WITH THE INDEX KA (OUTPUT)
         NEXT - NO. OF PROBLEM (INPUT)


      CALL EAHD22(N,KA,X,HA,NEXT)

         N - NUMBER OF VARIABLES (INPUT)
         KA - INDEX OF THE GIVEN FUNCTION IN THE SUM OF SQUARES (INPUT)
         X(N) - ACTUAL VECTOR OF VARIABLES (INPUT)
         HA(N*(N+1)/2) - HESSIAN MATRIX OF THE GIVEN FUNCTION WITH THE
                         INDEX KA (OUTPUT)
         NEXT - NO. OF PROBLEM (INPUT)


RECOMMENDED INPUT VALUES N=20 AND NA=163
