Main

## Main.OptionApmReduce History

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(:title APM.REDUCE - APMonitor Option:) (:keywords APM.REDUCE, Optimization, Estimation, Option, Configure, Default, Description:) (:description REDUCE is the number of cycles of pre-processing to analyze the problem structure and eliminate variables that can be fixed and equations that can be eliminated from the problem:)

 Type: Integer, Input
Default Value: 0
Description: Number of pre-processing cycles to identify
equations or variables to eliminate


REDUCE is the number of cycles of pre-solve analysis before sending the problem to a solver. The analysis eliminates variables and equations with the following characteristics:

• variables that don't belong to an equation or objective
• equations with assignments such as x=2.5 (set to value and fix)
• identified with a single non-zero in Jacobian row
• set variable equal to zero, evaluate residual
• then set x = -resid/jac (when abs(jac)>tolerance)
• check that upper or lower limits are not violated
• equations that connect two variables y = z (merge)
• set variables equal to zero, evaluate residual
• if abs(residual)~0 and abs(jac_1 - jac_2) ~ 0, merge
• independent blocks of linear equations (not yet implemented)
• perform Lower Block Triangularization (LBT)
• analyze independent blocks
• if equation blocks are linear then solve and fix

If no variables are left (all reduced) then APMonitor reports a successful solution without sending the problem to a solver. When no variables or equations are eliminated, the remainder of the REDUCE cycles are skipped. REDUCE has the potential to present a more dense and smaller problem to the solver but may also require more pre-processing time that is more efficiently utilized by the solver.