Modified Projected Newton Scheme for Non-convex Function with Simple Constraints

Abstract

In this paper, a descent line search scheme is proposed to find a local minimum point of a non-convex optimization problem with simple constraints. The idea ensures that the scheme escapes the saddle point and finally settles for a local minimum point of the non-convex optimization problem.
Positive definite scaling matrix for the proposed scheme is formed through symmetric indefinite
matrix factorization of the Hessian matrix of the objective function at each iteration. Numerical
illustrations are provided and global convergence of the scheme is also justified.