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...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 8; no. 4; p. 616
Main Authors: Lai, Kin Keung, Mishra, Shashi Kant, Ram, Bhagwat
Format: Journal Article
Language:English
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
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math8040616