An adjoint for likelihood maximization

The process of likelihood maximization can be found in many different areas of computational modelling. However, the construction of such models via likelihood maximization requires the solution of a difficult multi-modal optimization problem involving an expensive O(n(3)) factorization. The optimization techniques used to solve this problem may require many such factorizations and can result in a significant bottleneck. This article derives an adjoint formulation of the likelihood employed in the construction of a kriging model via reverse algorithmic differentiation. This adjoint is found to calculate the likelihood and all of its derivatives more efficiently than the standard analytical method and can therefore be used within a simple local search or within a hybrid global optimization to accelerate convergence and therefore reduce the cost of the likelihood optimization.