The Hamiltonian approach for constrained optimization is indeed a useful tool in the hands of the economists, scientists and statisticians who applied it in the modelling of optimization problems. It can be noted that the treatise in this research work is an eye opener for a better understanding, application and utilization of the method as we exploit its vitality to solving optimization problems. Though, the approach seems to be a derived approach from existed ones but also intensified a great sense of relief to the problem of continuous economics. Just as cited in this piece of work that “the assumption that economic activity takes place continuously is a convenient abstraction in many applications, the issue of solving macroeconomics with continuous problem has always lived the researcher with difficulties as real life situation cannot be modelled based on assumptions alone”. We have shown in this research work how the Hamiltonian approach is applied to solve continuous optimization problems. Thus, it should be cleared to us that the Hamiltonian approach is much appreciated when dealing with initial value problems with continuous time situations rather than the Lagrange, ordinary derivative, Newton Rapson, the penalty function, gradient projection and the quadratic programming method.