Bochner空间中的Optimization
Optimization in Bochner Spaces
摘要：
本文研究了一致凸、一致光滑Bochner空间中的若干最优化问题。我们考虑四种情况下的基础子集：闭和凸子集，闭和凸锥，闭子空间和闭球。在每种情况下，我们研究的存在性问题和逆像的性质。我们认为本文的结果和分析方法可应用于随机最优化、随机变分不等式和随机不动点理论。
英文摘要：
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.
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