Abstract: The optimization problem using time scales is studied.
Time scale is a model of time. The language of time scales seems to
be an ideal tool to unify the continuous-time and the discrete-time
theories. In this work we present necessary conditions for a solution
of an optimization problem on time scales. To obtain that result we
use properties and results of the partial diamond-alpha derivatives for
continuous-multivariable functions. These results are also presented
here.