Treating k-2 and k4 as adjustable parameters leads to a set of equality constraints for rate constants and enzyme forms (See Additional file 1 for details).
We denote by and the sets of equality constraints indices for which a corresponding Lagrange multiplier is positive and negative, respectively, that is, and.
As a consequence, the handling of equality constraints has long been a difficult issue for evolutionary optimization methods.
Using classical feedback control principle the LMI-based procedure is provided for computation of the gain matrix of state control laws, and influence of equality constraints is explained.
denotes the number of equality constraints.
It is noteworthy that ICDE adopts a fixed tolerance value for the equality constraints.
The set-monotonic algorithm contains a block for problems with equality constraints, and operates within the unit cube [0,1]n for all problems.
The set-monotonic algorithm contains a block for problems with equality constraints, and operates within the unit cube [0,1]n universal for all problems.
The penalty terms, with increasing multiplier sequence (alpha ^{ k)}), penalize for non-zero equality constraints and assist in driving the solution towards feasibility in terms of (4) and (5).
The resulting technique for incorporating parameter equality constraints into numerical simulation and optimization consistently reduces the number of parameters for a single enzyme, thereby ensuring maximum efficiency and robustness of the parameterization method.
