Given x 0 , a point of a convex subset C of a Euclidean space, the two following statements are proven to be equivalent: (i) every convex function f : C → ℝ is upper semi-continuous at x 0 , and (ii) ...

A simple expression is presented that is equivalent to the norm of the $L_v^p \to L_u^q$ embedding of the cone of quasi-concave functions in the case 0 < q < p < ∞ ...

Convex optimisation constitutes a fundamental area in applied mathematics where the objective is to identify the minimum of a convex function subject to a set of convex constraints. This framework ...

The concavity exercise asks students to think about erosion in natural forms and how that concavity contrasts with the convexity of the objects. Dominant, subdominant, and subordinate relationships ...