标题： 博赫纳空间中的优化 显示英文标题

标题： Optimization in Bochner Spaces

摘要： 在本文中，我们研究了均匀凸性和均匀光滑Bochner空间中的一些优化问题。 我们考虑了底层子集的四种情况：闭合且凸的子集、闭合且凸的锥体、闭合子空间和闭球。 在每种情况下，我们研究了存在性问题和逆像性质。 我们认为本文的结果和分析方法可以应用于随机优化、随机变分不等式和随机不动点理论。 显示英文摘要

摘要： In this paper, we study some optimization problems in uniformly convex and uniformly smooth Bochner spaces. We consider four cases of the underlying subsets: closed and convex subsets, closed and convex cones, closed subspaces and closed balls. In each case, we study the existence problems and the inverse image properties. We think that the results and the analytic methods in this paper could be applied to the theories of stochastic optimization, stochastic variational inequality and stochastic fixed point.