## Convexity Conditions of Kantorovich Function and Related Semi-infinite Linear Matrix Inequalities

The Kantorovich function $(x^TAx)( x^T A^{-1} x)$, where $A$ is a positive definite matrix, is not convex in general. From a matrix or convex analysis point of view, it is interesting to address the question: When is this function convex? In this paper, we prove that the 2-dimensional Kantorovich function is convex if and only … Read more

## Convexity Conditions and the Legendre-Fenchel Transform for the Product of Finitely Many Positive Definite Quadratic Forms

While the product of finitely many convex functions has been investigated in the field of global optimization, some fundamental issues such as the convexity condition and the Legendre-Fenchel transform for the product function remain unresolved. Focusing on quadratic forms, this paper is aimed at addressing the question: \emph{When is the product of finitely many positive … Read more