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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Veröffentlicht in:Mathematics (Basel) Jg. 8; H. 4; S. 616
Hauptverfasser: Lai, Kin Keung, Mishra, Shashi Kant, Ram, Bhagwat
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.04.2020
Schlagworte:
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
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Zusammenfassung: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