RESEARCH OF BICONVEX FUNCTIONS

This paper studies biconvex functions, which are pointwise upper bounds for some nonempty family of 2-affine, 2-linear, biaffine and bilinear functions, respectively. It is shown that biconvex functions are closely related to convex functions defined on the tensor product of spaces. This paper investigates the bisubdifferentiability of biconvex functions and studies several of their properties. The paper also studies the properties of biconjugate functions. The paper also studies the bisubdifferential of the maximum function. Using the second conjugate function on the tensor product of spaces, criteria for bisubdifferentiability of functions are obtained. The characterization of biconvex functions is considered.