A new efficient alternative extension of the Hager-Zhang conjugate gradient method for vector optimization
Optimization Eruditorum, Volume 3, Issue 1, April 2026, Pages 34–53
XIAOQING OU
College of Management, Chongqing College of Humanities, Science & Technology, Chongqing 401524, China
YUNYE WAN
Beibei Power Supply Branch of State Grid Chongqing Electric Power Company, Chongqing 400700, China
ZHAO-HAN LIU
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
HUILIN HAN
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
WEIGUANG PENG
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
JIAWEI CHEN
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
Abstract
In this paper, a new efficient alternative extension of the Hager-Zhang conjugate gradient method is proposed to solve the vector optimization problem that ensures sufficient descent without relying on any linear search or convexity assumptions. We give the convergence of our proposed method combined with Wolfe line search under mild assumptions. Finally, we show through numerical experiments that our proposed method is more efficient than the extant related vector Hagar-Zhang conjugate method.
Cite this Article as
Xiaoqing Ou, Yunye Wan, Zhao-Han Liu, Huilin Han, Weiguang Peng, Jiawei Chen, A new efficient alternative extension of the Hager-Zhang conjugate gradient method for vector optimization, Optimization Eruditorum, 3(1), 34–53, 2026