论文标题
关于卡利尔的不平等
On Carlier's inequality
论文作者
论文摘要
Fenchel-Young不平等在凸分析和优化中至关重要。它指出，两个向量的某些函数值与它们的内部产物之间的差异是无负的。最近，Carlier引入了这种不平等的非常好的锐化，提供了取决于正参数的下限。 在本说明中，我们通过三种方式扩展了Carlier的不平等。首先，提供了双重性声明。其次，我们讨论渐近行为，因为基础参数接近零或无穷大。第三，依靠环状单调性和相关的fitzpatrick功能，我们提出了一个较低的界限，其中具有无限的规范平方。几个例子说明了我们的结果。
The Fenchel-Young inequality is fundamental in Convex Analysis and Optimization. It states that the difference between certain function values of two vectors and their inner product is nonnegative. Recently, Carlier introduced a very nice sharpening of this inequality, providing a lower bound that depends on a positive parameter. In this note, we expand on Carlier's inequality in three ways. First, a duality statement is provided. Secondly, we discuss asymptotic behaviour as the underlying parameter approaches zero or infinity. Thirdly, relying on cyclic monotonicity and associated Fitzpatrick functions, we present a lower bound that features an infinite series of squares of norms. Several examples illustrate our results.
