Analysis of convergence for control problems governed by evolution equations inequality and equality constraints with multipliers imbedded

Convergence Ratio Profile for Optimal Control Problems Governed by Ordinary Differential Equations with Matrix Coefficients

“…Step In [6] , a general quadratic functional in the Hilbert Space H to be minimized as Since A is a self-adjoint operator, [2,7,8]…”

“…In [1,2] , the scheme establishing the solution of optimal control problems constrained by evolution equation of the delay type with matrix coefficients was presented, without addressing the geometric convergence ratio profile. Here, a class of optimal control problems constrained by ordinary differential equation with matrix coefficients is considered.…”

“…Using [4] , a penalty function method is applied to convert the constrained problem into an unconstrained formulation problem. With this formulation, an associated control operator was constructed as in [2] . Here, again, we state the constructed operator as a consequence of a theorem in this paper to allow for brevity and compactness of the paper.…”