An adjoint for likelihood maximization

Description/Abstract

The process of likelihood maximization can be found in many di®erent areas of computational modelling. However, the construction of such models via likelihood maximization requires the solution of a di±cult multi-modal optimization problem
involving an expensive O(n3) factorization. The optimization techniques used to solve this problem may require many such factorizations and can result in a significant bottle-neck. This article derives an adjoint formulation of the likelihood employed in the construction of a kriging model via reverse algorithmic diferentiation. This adjoint is found to calculate the likelihood and all of its derivatives more efficiently than the standard analytical method and can therefore be utilised within a simple local search or within a hybrid global optimization to accelerate
convergence and therefore reduce the cost of the likelihood optimization