@Article{JCM-42-24,
author = {Jauny , Ghosh , Debdas and Upadhayay , Ashutosh},
title = {A Newton-Type Globally Convergent Interior-Point Method to Solve Multi-Objective Optimization Problems},
journal = {Journal of Computational Mathematics},
year = {2023},
volume = {42},
number = {1},
pages = {24--48},
abstract = {<p style="text-align: justify;">This paper proposes an interior-point technique for detecting the nondominated points
of multi-objective optimization problems using the direction-based cone method. Cone
method decomposes the multi-objective optimization problems into a set of single-objective
optimization problems. For this set of problems, parametric perturbed KKT conditions
are derived. Subsequently, an interior point technique is developed to solve the parametric
perturbed KKT conditions. A differentiable merit function is also proposed whose stationary point satisfies the KKT conditions. Under some mild assumptions, the proposed
algorithm is shown to be globally convergent. Numerical results of unconstrained and constrained multi-objective optimization test problems are presented. Also, three performance
metrics (modified generational distance, hypervolume, inverted generational distance) are
used on some test problems to investigate the efficiency of the proposed algorithm. We
also compare the results of the proposed algorithm with the results of some other existing
popular methods.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2204-m2021-0241},
url = {http://global-sci.org/intro/article_detail/jcm/22151.html}
}