Pivot Tolerance
- Type
Floating point number
- Range
[0,1] + {na}
- Default
na
During the solve of QP subproblems, the pivot tolerance is used to prevent columns entering the basis if they would cause the basis to become almost singular.
When x changes to x+ap for some search direction p, a “ratio test” is used to determine which component of x reaches an upper or lower bound first. The corresponding element of p is called the pivot element. Elements of p are ignored (and therefore cannot be pivot elements) if they are smaller than the pivot tolerance.
It is common for two or more variables to reach a bound at essentially the same time. In such cases, the Feasibility Tolerance provides some freedom to maximize the pivot element and thereby improve numerical stability. Excessively small values for the Feasibility Tolerance should therefore not be specified. To a lesser extent, the Expand Frequency also provides some freedom to maximize the pivot element. Excessively large values for the Expand Frequency should therefore not be specified.
The default value of this option depends on the relative precision of the computer being used. On most computers the default equals 3.7e-11.
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