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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Vydáno v:Algorithms Ročník 18; číslo 7; s. 381
Hlavní autoři: Pandey, Rupesh Krishna, Upadhyay, Balendu Bhooshan, Poddar, Subham, Stancu-Minasian, Ioan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.07.2025
Témata:
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
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Shrnutí: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