When *T* is self-adjoint, we have* * the minimum of *k.*

When *m=3* and *T∈B(H) * , we obtain the minimum of *k* and an inequality

Involving the numerical radius *w(T)* .

$$f(x^*) = \min_{x \in X} f(x) \eqno (1)$$

where the function $f$ : $ \pmb{\mathbb{R}}^{n} \longrightarrow \pmb{\mathbb{R}}$ is convex on a closed convex set X.

In this work, we will give a new method to solve problem (1) without bringing it back to an unconstrained problem. We study the convergence of this new method and give numerical examples.