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SIGEST
SIAM Review ( IF 10.8 ) Pub Date : 2021-11-04 , DOI: 10.1137/21n975345 The Editors
SIAM Review ( IF 10.8 ) Pub Date : 2021-11-04 , DOI: 10.1137/21n975345 The Editors
SIAM Review, Volume 63, Issue 4, Page 781-781, January 2021.
The SIGEST article in this issue, which comes from the SIAM Journal on Control and Optimization (SICON), is “Convex Relaxation of Discrete Vector-Valued Optimization Problems,” by Christian Clason, Carla Tameling, and Benedikt Wirth. The authors tackle a new class of problems where a vector-valued control must take pointwise values in a given, finite set. The resulting optimization task involves a regularization term akin to the classical $L_1$ regularization that has been used to promote sparsity. This paper expertly combines techniques from optimal control theory, convex analysis, relaxation, and numerical algorithms. Meaningful computational examples involving nuclear magnetic resonance imaging and linearized elasticity are used to illustrate the theory. A further example concerning transport of material through a street or pipe network has been added to this SIGEST version in order to showcase the broad applicability of the approach beyond typical optimal control problems. MATLAB code is available for these experiments. The revision for SIGEST also includes extra details in section 4 on the explicit characterization of the convex penalty and its generalized derivatives for general constraint sets and a discussion on how to evaluate them algorithmically; this procedure in particular is used in the numerical computations on the new example. In addition, the authors have extended the abstract and introduction, and provided more details and references in sections 2 and 3 on convex analysis and Gamma convergence, and on related work that has been published since the original 2018 SICON version appeared.
中文翻译：
SIGEST
SIAM 评论，第 63 卷，第 4 期，第 781-781 页，2021 年 1 月。
本期 SIGEST 文章来自 SIAM Journal on Control and Optimization (SICON)，是“离散向量值优化问题的凸松弛”，作者为 Christian Clason、Carla Tameling 和 Benedikt Wirth。作者解决了一类新问题，其中向量值控件必须在给定的有限集合中采用逐点值。由此产生的优化任务涉及一个类似于经典的 $L_1$ 正则化项的正则化项，该正则化项已被用于促进稀疏性。本文巧妙地结合了最优控制理论、凸分析、松弛和数值算法的技术。使用涉及核磁共振成像和线性化弹性的有意义的计算示例来说明该理论。此 SIGEST 版本中添加了有关通过街道或管网运输材料的另一个示例，以展示该方法在典型优化控制问题之外的广泛适用性。MATLAB 代码可用于这些实验。SIGEST 的修订版还包括第 4 节中关于凸惩罚的显式特征及其一般约束集的广义导数的额外细节，以及关于如何从算法上评估它们的讨论；该程序特别用于新示例的数值计算。此外，作者还扩展了摘要和介绍，并在第 2 和第 3 节中提供了更多关于凸分析和 Gamma 收敛的详细信息和参考资料，
更新日期：2021-11-05
The SIGEST article in this issue, which comes from the SIAM Journal on Control and Optimization (SICON), is “Convex Relaxation of Discrete Vector-Valued Optimization Problems,” by Christian Clason, Carla Tameling, and Benedikt Wirth. The authors tackle a new class of problems where a vector-valued control must take pointwise values in a given, finite set. The resulting optimization task involves a regularization term akin to the classical $L_1$ regularization that has been used to promote sparsity. This paper expertly combines techniques from optimal control theory, convex analysis, relaxation, and numerical algorithms. Meaningful computational examples involving nuclear magnetic resonance imaging and linearized elasticity are used to illustrate the theory. A further example concerning transport of material through a street or pipe network has been added to this SIGEST version in order to showcase the broad applicability of the approach beyond typical optimal control problems. MATLAB code is available for these experiments. The revision for SIGEST also includes extra details in section 4 on the explicit characterization of the convex penalty and its generalized derivatives for general constraint sets and a discussion on how to evaluate them algorithmically; this procedure in particular is used in the numerical computations on the new example. In addition, the authors have extended the abstract and introduction, and provided more details and references in sections 2 and 3 on convex analysis and Gamma convergence, and on related work that has been published since the original 2018 SICON version appeared.
中文翻译：
SIGEST
SIAM 评论，第 63 卷，第 4 期，第 781-781 页，2021 年 1 月。
本期 SIGEST 文章来自 SIAM Journal on Control and Optimization (SICON)，是“离散向量值优化问题的凸松弛”，作者为 Christian Clason、Carla Tameling 和 Benedikt Wirth。作者解决了一类新问题，其中向量值控件必须在给定的有限集合中采用逐点值。由此产生的优化任务涉及一个类似于经典的 $L_1$ 正则化项的正则化项，该正则化项已被用于促进稀疏性。本文巧妙地结合了最优控制理论、凸分析、松弛和数值算法的技术。使用涉及核磁共振成像和线性化弹性的有意义的计算示例来说明该理论。此 SIGEST 版本中添加了有关通过街道或管网运输材料的另一个示例，以展示该方法在典型优化控制问题之外的广泛适用性。MATLAB 代码可用于这些实验。SIGEST 的修订版还包括第 4 节中关于凸惩罚的显式特征及其一般约束集的广义导数的额外细节，以及关于如何从算法上评估它们的讨论；该程序特别用于新示例的数值计算。此外，作者还扩展了摘要和介绍，并在第 2 和第 3 节中提供了更多关于凸分析和 Gamma 收敛的详细信息和参考资料，
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