In formulating the optimization problem, first we need convenient variables to represent the concentrations and rate constants in the kinetic model. Let the vector x be the state variables that correspond to the species concentrations. In brackets are the physically reasonable ranges for each of the state variables.

We define the vector q to represent the known constants in the system.

Also, let the vector p represent the adjustable or unknown values in the system. In the brackets are the physically reasonable bounds for the variables.

The data vector d consists of the average value of the absorbance at each time-point in the vector t and has an error estimate based on the replicate values of absorbance σ.

The model is formed from the rules for elementary rates in kinetics.

Initial conditions for the model are based on the experimental values for the reactants.

Finally, using the known values of the absorbance for cyclohexadienyl radical and a value for the background absorbance we can create an objective function for comparing the data at each point with the state variables in the model. Let i be the index corresponding to each data point.