Application of Derivatives to Nonlinear Programming for Prescriptive Analytics

Gone are the days when business analytics would bank on statistics alone. Besides the traditional probability theory and statistics, the machine learning techniques of the present era, work in complete sync with linear algebra, graph theory, dynamic programming, multivariate calculus etc. As far as multivariate calculus is concerned, the different methods that lend support to machine learning algorithms are differential and integral calculus, partial derivatives, gradient and directional derivative, vector-valued function, Jacobian matrix and determinant, Hessian matrix, Laplacian and Lagrangian distributions etc. The present article will discuss the applications of second order derivatives and partial derivatives on optimization problems, as required for prescriptive analytics.