These identities including the Cassini type identity and Honsberger type formula can be applied to some polynomial

sequences such as Fibonacci polynomials, Lucas polynomials, Pell polynomials, Pell-Lucas polynomials and so on, which

generalize the previous results in references.]]>

results obtained in ( Roamba, Zabsonré & Zongo, 2017) . However, our model does not take into account cold pressure

term and the quadratic friction term as in (Roamba, Zabsonré & Zongo, 2017) which are considered regularizing terms to

show the existence of global weak solutions of your model. Without these regularizing terms, we show the existence of

global weak solutions in time with a periodic domain.]]>

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

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

To solve problem (1), most methods transform this problem into a problem without constraints, either by introducing Lagrange multipliers or a projection method.

The purpose of this paper is to give a new method to solve some constrained optimization problems, based on the definition of a descent direction and a step while remaining in the X convex domain. A convergence theorem is proven. The paper ends with some numerical examples.