fmincon performance with linear vs non linear constraints
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I am currently running fmincon interior point with linear inqeuality, equality and non-linear inequality constraints. I am specifying both objective gradient and constraint gradient. I am wondering if there is any benefit with regard to speed up if I specify the linear inequality constraint as a non-linear inequality constraint along with the corresponding gradient.
In general, specifying a linear inequality constraint as a non-linear inequality constraint with corresponding gradient may not lead to a significant speedup in ‘fmincon’ interior point algorithm. This is because ‘fmincon’ interior point algorithm is specifically designed to handle linear inequality constraints efficiently.
The benefit of specifying non-linear constraints (and their gradients) may arise in cases where the constraints themselves are non-linear in nature. In such cases, providing the non-linear gradient can help ‘fmincon’ to converge faster.
However, if you are uncertain about the linearity of your inequality constraint, or if you suspect that there may be some non-linearity, it is worth trying both linear and non-linear formulations of the constraint to see if there is any significant difference in the performance and convergence rate of ‘fmincon’.
Hope this helps,