The Penalty Cost Functional for the Two-Dimensional Energized Wave Equation

This paper constructs the penalty cost functional for optimizing the two-dimensional control operator of the energized wave equation. In some multiplier methods such as the Lagrange multipliers and Pontrygean maximum principle, the cost of merging the constraint equation to the integral quadratic objective functional to obtain an unconstraint equation is normally guessed or obtained from the first partial derivatives of the unconstrained equation. The Extended Conjugate Gradient Method (ECGM) necessitates that the penalty cost be sequentially obtained algebraically. The ECGM problem contains a functional which is completely given in terms of state and time spatial dependent variables.