On q-Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems

A parameter-free optimization technique is applied in Quasi-Newton’s method for solving unconstrained multiobjective optimization problems. The components of the Hessian matrix are constructed using q-derivative, which is positive definite at every iteration. The step-length is computed by an Armijo...

Full description

Saved in:
Bibliographic Details
Published inMathematics (Basel) Vol. 8; no. 4; p. 616
Main Authors Lai, Kin Keung, Mishra, Shashi Kant, Ram, Bhagwat
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.04.2020
Subjects
Algorithms
Calculus
Hessian matrices
Interdisciplinary subjects
Iterative methods
Matrix methods
Methods
methods of quasi-Newton type
multiobjective programming
Multiple objective analysis
Nonlinear programming
Optimization
Optimization techniques
Pareto optimality
q-calculus
rate of convergence
Online AccessGet full text

Cover

More Information
Summary:A parameter-free optimization technique is applied in Quasi-Newton’s method for solving unconstrained multiobjective optimization problems. The components of the Hessian matrix are constructed using q-derivative, which is positive definite at every iteration. The step-length is computed by an Armijo-like rule which is responsible to escape the point from local minimum to global minimum at every iteration due to q-derivative. Further, the rate of convergence is proved as a superlinear in a local neighborhood of a minimum point based on q-derivative. Finally, the numerical experiments show better performance.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8040616