条件下确界、隐凸性与S-过程

中文摘要 AI 辅助

检测隐凸性是解决非凸最小化问题并寻找全局最小化器的工具之一。我们引入了条件下确界的概念，发展了相关理论，并建立了与最小化问题相关的塔性质。然后，我们说明了条件下确界在揭示隐凸性方面如何发挥关键作用。由此，我们为非凸二次最小化问题中的隐凸性提供了一个新的充分条件，该条件涵盖并超越了已知结果（借助块符号对矩阵-向量的概念）。我们还展示了条件下确界如何特别适用于处理所谓的S-过程。

英文摘要

Detecting hidden convexity is one of the tools to address nonconvex minimization problems, and find global minimizers. We introduce the notion of conditional infimum, develop the theory, and establish a tower property, relevant for minimization problems. Then, we illustrate how the conditional infimum is instrumental in revealing hidden convexity. Thus equipped, we provide a new sufficient condition for hidden convexity in nonconvex quadratic minimization problems, that encompasses and goes beyond known results (with the notion of block-signed pair matrix-vector). We also show how the conditional infimum is especially adapted to tackle the so-called S-procedure.

发表机构

• Cermics, École nationale des ponts et chaussées, IP Paris（Cermics，国立桥梁学校，巴黎理工学院）

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