If you use bad initial values for the parameters, the computation of the value of the objective function (and its derivatives) can lead to arithmetic overflows in the first iteration. The line-search algorithms that work with cubic extrapolation are especially sensitive to arithmetic overflows. If an overflow occurs with an optimization technique that uses line search, you can use the INSTEP= option to reduce the length of the first trial step during the line search of the first five iterations or use the DAMPSTEP or MAXSTEP= option to restrict the step length of the initial in subsequent iterations. If an arithmetic overflow occurs in the first iteration of the trust region, double dogleg, or Levenberg-Marquardt algorithm, you can use the INSTEP= option to reduce the default trust region radius of the first iteration. You can also change the minimization technique or the line-search method. If none of these methods helps, consider the following actions:

The starting point must be a point that can be evaluated by all the functions involved in your problem. However, during optimization the optimizer may iterate to a point where the objective function or nonlinear constraint functions and their derivatives cannot be evaluated. If you can identify the problematic region, you can prevent the algorithm from reaching it by adding another constraint to the problem. Another possibility is a modification of the objective function that will produce a large, undesired function value. As a result, the optimization algorithm reduces the step length and stays closer to the point that has been evaluated successfully in the previous iteration. For more information, refer to the section Missing Values in Program Statements.

The sequential quadratic programming algorithm in QUANEW, which is used for solving nonlinearly constrained problems, can have problems updating the Lagrange multiplier vector . This usually results in very high values of the Lagrangian function and in watchdog restarts indicated in the iteration history. If this happens, there are three actions you can try:

There are a number of things to try if the optimizer fails to converge.

The (projected) gradient at a stationary point is zero and that results in a zero step length. The stopping criteria are satisfied.

There are two ways to avoid this situation:

The signs of the eigenvalues of the (reduced) Hessian matrix contain information regarding a stationary point:

In some applications, PROC NLP may result in parameter estimates that are not precise enough. Usually this means that the procedure terminated too early at a point too far from the optimal point. The termination criteria define the size of the termination region around the optimal point. Any point inside this region can be accepted for terminating the optimization process. The default values of the termination criteria are set to satisfy a reasonable compromise between the computational effort (computer time) and the precision of the computed estimates for the most common applications. However, there are a number of circumstances where the default values of the termination criteria specify a region that is either too large or too small. If the termination region is too large, it can contain points with low precision. In such cases, you should inspect the log or list output to find the message stating which termination criterion terminated the optimization process. In many applications, you can obtain a solution with higher precision by simply using the old parameter estimates as starting values in a subsequent run where you specify a smaller value for the termination criterion that was satisfied at the previous run.

If the termination region is too small, the optimization process may take longer to find a point inside such a region or may not even find such a point due to rounding errors in function values and derivatives. This can easily happen in applications where finite-difference approximations of derivatives are used and the GCONV and ABSGCONV termination criteria are too small to respect rounding errors in the gradient values.