In this paper we propose two algorithms based on branch and bound method and reduced interval techniques to compute all real zeros of a polynomial. Quadratic bounding functions are proposed which are better than the well known linear underestimator. Experimental result shows the efficiency of the two algorithms when facing ill-conditionned polynomials.
The paper is concerned with the multivariate global optimization with box constraints. A new underestimator is investigated for twice continuously differentiable function on a box which is an extension of the approach developed in  for univariate global optimization.
In this paper we propose an efficient approach for globally solving a class of convex semi-infinite programming (SIP) problems. Under the objective function and constraints (w.r.t. the variables to be optimized) convexity assumption, and appropriate differentiability, we propose a branch and bound exchange type method for SIP. To compute a feasible point… (More)