When general constraints are present, a sequence of augmented Lagrangian functions are (approximately) optimized until the solution to the original problem is determined. At the end of each (approximate) optimization, either the penalty parameter is reduced or improved Lagrange multiplier estimates are accepted. The method is designed so that ultimately only the latter possibility may occur. When the algorithm is far from the solution to the original problem, there may not be any point in accepting Lagrange multiplier estimates as they may be very inaccurate and it may be preferable to reduce the penalty parameter instead.
If the user includes the DECREASE-PENALTY-PARAMETER-UNTIL< keyword, no multiplier estimates will be accepted until the penalty parameter has been reduced to below the real value following the keyword. Likewise, no multiplier estimates will be accepted until the norms of the projected gradients and constraints are smaller than the values following the keywords FIRST-CONSTRAINT-ACCURACY-REQUIRED and FIRST-GRADIENT-ACCURACY-REQUIRED respectively. Defaults of