BORDERED HESSIAN METHOD For Constrained Optimisation Numerical. #Hessian #optimisation

A bordered Hessian matrix is a matrix that is derived from the Hessian matrix of a function. The Hessian matrix is a square matrix of second partial derivatives of a function, and it is used to characterize the local curvature of the function at a given point. The bordered Hessian matrix is a matrix that is formed by adding rows and columns to the Hessian matrix. These additional rows and columns may contain additional partial derivatives or other quantities that are related to the function being considered. The bordered Hessian matrix is often used in optimization problems, where it can provide additional information about the behavior of the function near a given point. In general, the bordered Hessian matrix can be used to perform a variety of tasks, such as finding stationary points of a function, identifying local minima or maxima, or identifying saddle points. It can also be used to perform sensitivity analysis, which involves studying how the output of a function changes as the input variables are varied