Let X be a uniformly smooth and 2-uniformly convex real Banach space with dual space $X^{\ast }$. In this paper, a Halpern-type subgradient extragradient algorithm is constructed. The sequence, generated by the algorithm, converges strongly to a common solution of variational inequality and two convex minimization problems. This result is obtained as an application of a Halpern-type subgradient extragradient algorithm, for approximating a common solution of variational inequality and J-fixed points of two continuous J-pseudocontractions. The theorem proved complements, improves and unifies many recent results in the literature. Finally, numerical experiments are given to illustrate the convergence of the sequence generated by the algorithm.

设X是一个具有对偶空间的均匀光滑且 2-均匀凸的实 Banach 空间$X^{＊}$. 本文构建了一种Halpern型次梯度超梯度算法。由算法生成的序列强烈收敛于变分不等式和两个凸最小化问题的共同解。该结果是作为 Halpern 型次梯度超梯度算法的应用获得的，用于逼近两个连续J伪收缩的变分不等式和J 不动点的公共解。该定理证明补充、改进和统一了文献中的许多最新结果。最后通过数值实验说明算法生成的序列的收敛性。