*(English)*Zbl 1003.90030

From the authors’ abstract: “Let $\text{Conv}\left(X\right)$ be the set of the convex functionals defined on a linear space $X$, with values in $\mathbb{R}\cup \{+\infty \}\xb7$ In this paper we give an extension of the notion of duality for (convex) functionals to mappings which operate from $\text{Conv}\left(X\right)\times \text{Conv}\left(X\right)$ into $\text{Conv}\left(X\right)\xb7$

Afterwards, we present an algorithm which associates, under convenient assumptions, a self-dual operator to a given operator and its dual.”

The algorithm can be understood as an adaptation of the classical Newton type procedure to compute the square root. The authors’ iterative method approximates in particular a square root of a convex functional, but the idea has a much wider scope as is illustrated by several geometric examples.

##### MSC:

90C25 | Convex programming |

46A20 | Duality theory of topological linear spaces |

26B25 | Convexity and generalizations (several real variables) |

52A05 | Convex sets without dimension restrictions (convex geometry) |