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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| Published in | Mathematics (Basel) Vol. 8; no. 4; p. 616 |
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| Format | Journal Article |
| Language | English |
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| Abstract | 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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| AbstractList | 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. |
| Author | Lai, Kin Keung Mishra, Shashi Kant Ram, Bhagwat |
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| SubjectTerms | 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 |
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| Title | On q-Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems |
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