Next Article in Journal
Bohr Radius Problems for Some Classes of Analytic Functions Using Quantum Calculus Approach
Previous Article in Journal
Almost Sure Convergence for the Maximum and Minimum of Normal Vector Sequences
Previous Article in Special Issue
Detecting Extreme Values with Order Statistics in Samples from Continuous Distributions
Open AccessArticle

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

by Kin Keung Lai 1,*,†, Shashi Kant Mishra 2,† and Bhagwat Ram 3,†
1
College of Economics, Shenzhen University, Shenzhen 518060, China
2
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
3
DST-Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi 221005, India
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(4), 616; https://doi.org/10.3390/math8040616
Received: 1 April 2020 / Revised: 11 April 2020 / Accepted: 13 April 2020 / Published: 17 April 2020
(This article belongs to the Special Issue Numerical Methods)
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. View Full-Text
Keywords: multiobjective programming; methods of quasi-Newton type; Pareto optimality; q-calculus; rate of convergence multiobjective programming; methods of quasi-Newton type; Pareto optimality; q-calculus; rate of convergence
Show Figures

Figure 1

MDPI and ACS Style

Lai, K.K.; Mishra, S.K.; Ram, B. On q-Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems. Mathematics 2020, 8, 616.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop