A trust-region scheme for constrained multi-objective optimization problems with superlinear convergence property

Abstract

In this paper, a numerical approximation method is developed to find approximate solutions to a class of constrained multi-objective optimization problems. All the functions of the problem are not necessarily convex functions. At each iteration of the method, a particular type of subproblem is solved using the trust region technique, and the step is evaluated using the notions of actual reduction and predicted reduction. A non-differentiable $l_{\mathrm{\infty }}$ penalty function restricts the constraint violations. An adaptive BFGS update formula is introduced. Global convergence of the proposed algorithm is established under the Mangasarian-Fromovitz constraint qualification and some mild assumptions. Furthermore, it is justified that the proposed algorithm displays a super-linear convergence rate. Numerical results are provided to show the efficiency of the algorithm in the quality of the approximated Pareto front.

Keywords:

• Trust-region technique
• constrained multi-objective optimization
• Pareto front
• superlinear convergence

2020 Mathematics Subject Classifications:

• 90C29
• 90C30
• 65K05
• 49M37

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability

The data sets generated during the current study are available from the corresponding author upon reasonable request.

Additional information

Notes on contributors

Nantu Kumar Bisui

Nantu Kumar Bisui is pursuing a Ph.D. in the Department of Mathematics at the Indian Institute of Technology Kharagpur, India. He is working on multi-objective optimization problems under the guidance of Prof. Geetanjali Panda. His research focuses on developing, analyzing, and implementing numerical approximation algorithms for solving multiobjective optimization problems.

Geetanjali Panda

Geetanjali Panda is a Professor in the Department of Mathematics at the Indian Institute of Technology Kharagpur, India. She has published over 50 research papers. Her research focuses on developing numerical approximation algorithms for continuous optimization problems, including singleobjective and multi-objective cases.