Principle extremum of full action in electrodynamic

Here we are going to formulate and prove variational extremum principle for electrodynamics, asserting that there exists a functional that depends on powers. This functional always has a single extremum, and the necessary and sufficient conditions of this extremum existence are represented by Maxwell equations. This principle is realized also in the case when the system contains magnetic charges and magnetic currents. Besides, this principle is valid also if there are heat losses in the system. The method for solving the Maxwell equations system by gradient descent to extremum is indicated.