Convex analysis | Types of functions | Matrices

Polyconvex function

In mathematics, the notion of polyconvexity is a generalization of the notion of convexity for functions defined on spaces of matrices. Let Mm×n(K) denote the space of all m × n matrices over the field K, which may be either the real numbers R, or the complex numbers C. A function f : Mm×n(K) → R ∪ {±∞} is said to be polyconvex if can be written as a convex function of the p × p subdeterminants of A, for 1 ≤ p ≤ min{m, n}. Polyconvexity is a weaker property than convexity. For example, the function f given by is polyconvex but not convex. (Wikipedia).

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From playlist Analysis and its Applications

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Convex function | Complex number | Mathematics | Function (mathematics) | Determinant | Real number | Matrix (mathematics)