By solving the first equation in (60) we find [P.sub.i], that allows us to calculate the cost function
value [J.sub.i] and compare it to the desired [J.sup.*.sub.i], if the error isn't small enough the process is repeated using the new calculated state values [x.sub.i].
To alleviate blurring of the restored image caused by video dehazing, we add an edge intensity function to Kim et al.'s total cost function
because the edge is clearer after dehazing.
The first part is an estimation of coefficients for a translog cost function
to determine which factors contribute to economies of scale and the extent to which they contribute for each of the four years in the period 2012 to 2015.
The appropriate cost metric is a functionally equivalent cost function
which shows the least total cost of providing a given number of units of electricity with certainty.
During the iterative minimization of the cost function
, the parameters are optimized with the steepest descent method.
Based on (13), we can get the gradient of the cost function
on the initial conditions of pollutant concentration [C.sup.0.sub.i,j,k] 
The objective function was defined as a fuel consumption problem by considering the cost function
as an average velocity.
By assuming [sigma](t) = [y.sub.1] on [0, [T.sub.1]], we find that [y.sub.1] minimizes the following cost function
The cost function
we estimate for local public health services embodies this balancing process, and for this reason, it is an ideal tool for estimating economies of scale and scope as it assumes LHJs are doing their best in choosing inputs to balance the benefits of using all inputs.
First, it gathers the information about resource supply from the suppliers in order to construct a resource cost function
. Then it asks every house representative agent it has connection to as to what is her preferred consumption.
Looking at Figure 2, it appears the data doesn't have drastic swings (which suggests that a linear cost function
is plausible) and that there are no apparent outliers in the data set.