Optimization Toolbox

Preprocessing

A number of preprocessing steps occur before the actual iterative algorithm begins. The resulting transformed problem is one where:

• All variables are bounded below by zero.
• All constraints are equalities.
• Fixed variables, those with equal upper and lower bounds, are removed.
• Rows of all zeros in the constraint matrix are removed.
• The constraint matrix has full structural rank.
• Columns of all zeros in the constraint matrix are removed.
• When a significant number of singleton rows exist in the constraint matrix, the associated variables are solved for and the rows removed.

While these preprocessing steps can do much to speed up the iterative part of the algorithm, if the Lagrange multipliers are required, the preprocessing steps must be "undone" since the multipliers calculated during the algorithm are for the transformed, and not the original, problem. Thus, if the multipliers are not requested, this transformation back will not be computed, and may save some time computationally.

Main Algorithm

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