Convergence profile of a discretized scheme for constrained problem via the penalty-multiplier method

Abstract

An extended discretized scheme is proposed to examine the convergence
profile of a quadratic control problem constrained by evolution equation with real coefficients. With an unconstrained formulation of the problem via the penaltymultiplier method, the discretization of the time interval and differential constraint is carried out. An operator, to circumvent the cumbersome calculation inherent in some earlier schemes, such as the function space algorithm, is established and proved. An example is considered to test the effectiveness and superiority of this scheme as it
compares to other schemes in terms of convergence profile.