We investigate the minima of functionals of the form $$\int_{[a,b]}g(\dot u(s)){\rm d}s$$ where g is strictly convex. The admissible functions $u:[a,b]\longrightarrow\mathbb{R}$ are not necessarily convex and satisfy $u\leq f$ on [a,b], u(a)=f(a), u(b)=f(b), f is a fixed function on [a,b]. We show that the minimum is attained by $\bar f$, the convex envelope of f.

The signed similarities aggregation problem is solved with a boolean method derived from the Faure and Malgrange algorithm. The method is adequate either for integer similarities or real similarites, and multiple solutions can be enumerated. It needs a space amount equal to three times the input data size.