What Is Optimization Toolbox?

4 Large-Scale AlgorithmsThe algorithm then repeats these steps until the iterates converge. The mainstopping criteria is a standard onewhereare the primal residual, dual residual, and upper-bound feasibilityrespectively, andis the difference between the primal and dual objective values, and tol is sometolerance. The sum in the stopping criteria measures the total relative errorsin the optimality conditions in Equation 4-18.PreprocessingA number of preprocessing steps occur before the actual iterative algorithmbegins. 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.4-18