number of variables

number of inequality constraints

Initial values of the variables must be set in X(1),X(2),...,X(N). On return they will be changed to the solution.

reasonable initial change to variables (see description of RHO)

required accuracy (see description of RHO)

IPRINT should be set to 0, 1, 2 or 3, which controls the amount of printing during the calculation. Specifically, there is no output if IPRINT=0 and there is output only at the end of the calculation if IPRINT=1. Otherwise each new value of RHO and SIGMA is printed. Further, the vector of variables and some function information are given either when RHO is reduced or when each new value of F(X) is computed in the cases IPRINT=2 or IPRINT=3 respectively. Here SIGMA is a penalty parameter, it being assumed that a change to X is an improvement if it reduces the merit function F(X)+SIGMA*MAX(0.0,-C1(X),-C2(X),...,-CM(X)), where C1,C2,...,CM denote the constraint functions that should become nonnegative eventually, at least to the precision of RHOEND. In the printed output the displayed term that is multiplied by SIGMA is called MAXCV, which stands for 'MAXimum Constraint Violation'.

MAXFUN is an integer variable that must be set by the user to a limit on the number of calls of CALCFC. The value of MAXFUN will be altered to the number of calls of CALCFC that are made.

In order to define the objective and constraint functions, we require a subroutine that has the name and arguments SUBROUTINE CALCFC (N,M,X,F,CON) DIMENSION X(),CON() The values of N and M are fixed and have been defined already, while X is now the current vector of variables. The subroutine should return the objective and constraint functions at X in F and CON(1),CON(2), ...,CON(M). Note that we are trying to adjust X so that F(X) is as small as possible subject to the constraint functions being nonnegative.