Hestenes–Stiefel-Type Conjugate Direction Algorithm for Interval-Valued Multiobjective Optimization Problems

This article investigates a class of interval-valued multiobjective optimization problems (IVMOPs). We define the Hestenes–Stiefel (HS)-type direction for the objective function of IVMOPs and establish that it has a descent property at noncritical points. An Armijo-like line search is employed to de...

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Bibliographic Details
Published in:Algorithms Vol. 18; no. 7; p. 381
Main Authors: Pandey, Rupesh Krishna, Upadhyay, Balendu Bhooshan, Poddar, Subham, Stancu-Minasian, Ioan
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.07.2025
Subjects:
Algorithms
conjugate direction method
Conjugates
Convergence
Efficiency
generalized Hukuhara derivative
Hestenes–Stiefel method
interval-valued optimization
Linear equations
Mathematical functions
multiobjective optimization
Multiple objective analysis
Optimization
Optimization techniques
Pareto optimum
ISSN:1999-4893, 1999-4893
Online Access:Get full text
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Summary:This article investigates a class of interval-valued multiobjective optimization problems (IVMOPs). We define the Hestenes–Stiefel (HS)-type direction for the objective function of IVMOPs and establish that it has a descent property at noncritical points. An Armijo-like line search is employed to determine an appropriate step size. We present an HS-type conjugate direction algorithm for IVMOPs and establish the convergence of the sequence generated by the algorithm. We deduce that the proposed algorithm exhibits a linear order of convergence under appropriate assumptions. Moreover, we investigate the worst-case complexity of the sequence generated by the proposed algorithm. Furthermore, we furnish several numerical examples, including a large-scale IVMOP, to demonstrate the effectiveness of our proposed algorithm and solve them by employing MATLAB. To the best of our knowledge, the HS-type conjugate direction method has not yet been explored for the class of IVMOPs.
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ISSN:1999-4893
1999-4893
DOI:10.3390/a18070381