On Uniform Convexity, Total Convexity and Convergence of the Proximal Point and Outer Bregman Projection Algorithms in Banach Spaces
On Uniform Convexity, Total Convexity and Convergence of the Proximal Point and Outer Bregman Projection Algorithms in Banach Spaces
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发表时间：
2003
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通讯作者：
D. Butnariu;A. Iusem;C. Zălinescu
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作者：
D. Butnariu;A. Iusem;C. Zălinescu
本文研究并比较了函数在点处一致凸性和函数在有界集上一致凸性与函数在点处全凸性和函数序列相容性的概念。我们建立这些概念之间的联系，严格凸inflnite维设置和使用的连接，以获得改善的收敛结果，关于外Bregman投影算法解决凸可行性问题和广义邻近点算法在Banach空间中的优化。
In this paper we study and compare the notions of uniform convexity of functions at a point and on bounded sets with the notions of total convexity at a point and sequential consistency of functions, respectively. We establish connections between these concepts of strict convexity in inflnite dimensional settings and use the connections in order to obtain improved convergence results concerning the outer Bregman projection algorithm for solving convex feasibility problems and the generalized proximal point algorithm for optimization in Banach spaces.