Open AccessModified projected Newton scheme for non-convex function with simple constraints
Author(s) -
Suvra Kanti Chakraborty,
Geetanjali Panda
Publication year - 2021
Publication title -
yugoslav journal of operations research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.221
H-Index - 21
eISSN - 1820-743X
pISSN - 0354-0243
DOI - 10.2298/yjor200515002c
Subject(s) - hessian matrix , saddle point , mathematics , line search , mathematical optimization , simple (philosophy) , scheme (mathematics) , conic optimization , convergence (economics) , matrix (chemical analysis) , convex optimization , descent direction , convex function , newton's method , quasi newton method , function (biology) , regular polygon , gradient descent , convex combination , computer science , mathematical analysis , quantum mechanics , physics , nonlinear system , philosophy , materials science , computer security , economic growth , composite material , biology , geometry , epistemology , machine learning , evolutionary biology , artificial neural network , radius , economics
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 points and finally settles for a local minimum point of the non-convex optimization problem. A 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. A numerical illustration is provided, and the global convergence of the scheme is also justified.