A New Hybrid Conjugate Gradient Method Based on a Convex Combination for Multiobjective Optimization

Jamilu Yahaya (), Poom Kumam () and Mahmoud Muhammad Yahaya ()
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Jamilu Yahaya: King Mongkut’s University of Technology Thonburi (KMUTT)
Poom Kumam: King Mongkut’s University of Technology Thonburi (KMUTT)
Mahmoud Muhammad Yahaya: King Mongkut’s University of Technology Thonburi (KMUTT)

SN Operations Research Forum, 2025, vol. 6, issue 2, 1-26

Abstract: Abstract Conjugate gradient methods are a crucial class of techniques for solving unconstrained optimization problems. While the Hestenes-Stiefel and other conjugate gradient methods have recently been extended to multiobjective optimization setting-notably the Hestene-Stiefel failed to ensure descent direction. In contrast, the Conjugate Descent method consistently ensures a descent direction in this context. In this paper, we introduce a hybrid conjugate gradient method that combines a modified Hestenes-Stiefel method with the Conjugate Descent method through a convex combination. The convex coefficient parameter is derived using the Dai-Liao conjugacy condition and the condition for Newton’s direction. Crucially, this hybrid approach guarantees sufficient descent property under the Wolfe line search conditions while establishing global convergence under mild assumptions-without necessarily requiring an algorithmic restarts or assuming convexity on the objective functions. Preliminary numerical results demonstrate the clear advantages of this hybrid method over some existing conjugate gradient techniques.

Keywords: Conjugate gradient method; Hybrid conjugate gradient; Multiobjective optimization; Sufficient descent condition; 49M37; 90C29; 90C52; 90C30; 90C26 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s43069-025-00484-3

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