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Nonlinear Optimization Examples

Definition of Return Codes

The return code, which is represented by the output parameter rc in the optimization subroutines, indicates the reason for optimization termination. A positive value indicates successful termination, while a negative value indicates unsuccessful termination. Table 14.1 gives the reason for termination associated with each return code.

Table 14.1 Summary of Return Codes

Code

Reason for Optimization Termination

1

ABSTOL criterion satisfied (absolute F convergence)

2

ABSFTOL criterion satisfied (absolute F convergence)

3

ABSGTOL criterion satisfied (absolute G convergence)

4

ABSXTOL criterion satisfied (absolute X convergence)

5

FTOL criterion satisfied (relative F convergence)

6

GTOL criterion satisfied (relative G convergence)

7

XTOL criterion satisfied (relative X convergence)

8

FTOL2 criterion satisfied (relative F convergence)

9

GTOL2 criterion satisfied (relative G convergence)

10

linear independent constraints are active at xr and none of them could be released to improve the function value

-1

objective function cannot be evaluated at starting point

-2

derivatives cannot be evaluated at starting point

-3

objective function cannot be evaluated during iteration

-4

derivatives cannot be evaluated during iteration

-5

optimization subroutine cannot improve the function value (this is a very general formulation and is used for various circumstances)

-6

there are problems in dealing with linearly dependent active constraints (changing the LCSING value in the par vector can be helpful)

-7

optimization process stepped outside the feasible region and the algorithm to return inside the feasible region was not successful (changing the LCEPS value in the par vector can be helpful)

-8

either the number of iterations or the number of function calls is larger than the prespecified values in the tc vector (MAXIT and MAXFU)

-9

this return code is temporarily not used (it is used in PROC NLP where it indicates that more CPU than a prespecified value was used)

-10

a feasible starting point cannot be computed

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