A three-term Polak-Ribi\`ere-Polyak conjugate gradient method for vector optimization
Abstract
A novel three-term Polak-Ribi\`ere-Polyak conjugate gradient method is proposed for solving vector optimization problems. It should be emphasized that this is the first extension of three-term conjugate gradient methods from scalar optimization to vector optimization. The method can consistently generate a sufficient descent direction independent of line search procedures and without modifying the conjugate parameters. This result improves upon the corresponding conclusions in SIAM J. Optim. 28, 2690-2720 (2018), J. Optim. Theory Appl. 204,13 (2025) and Optim. Methods Softw. 28, 725-754 (2025). Based on a new Wolfe-type line search, the global convergence of the proposed scheme is established without imposing restrictions such as self-adjusting strategies, regular restarts and convexity assumptions. Numerical experiments demonstrate the favourable performance of the proposed method.
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