This survey contains recent developments for computing verified results of convex constrained optimization problems, with emphasis on applications. Especially, we consider the computation of verified error bounds for non-smooth convex conic optimization in the framework of functional analysis, for linear programming, and for semidefinite programming. A discussion of important problem transformations to special types of convex problems and convex relaxations is included. The latter are important for handling and for reliability issues in global robust and combinatorial optimization. Some remarks on numerical experiences, including also large-scale and ill-posed problems, and software for verified computations concludes this survey.

中文翻译：

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凸规划中验证的数值计算

该调查包含计算凸约束优化问题的验证结果的最新进展，重点是应用。特别是，我们考虑了在泛函分析、线性规划和半定规划框架中非光滑凸圆锥优化的验证误差界的计算。包括对特殊类型凸问题和凸松弛的重要问题转换的讨论。后者对于处理全局鲁棒性和组合优化中的可靠性问题很重要。对数值经验的一些评论，包括大规模和不适定的问题，以及用于验证计算的软件，结束了本调查。