The preferences of an agent can be expressed in various ways. The agent may indicate goals having different levels of priority for him, or provides classes of choices with their level of satisfaction for him. The first type of specification can be captured in possibilistic logic under the form of constraints on a necessity measure. It is shown in this paper that the second manner for expressing...

We propose two semismooth Newton methods for seeking the eigenvalues of a linear transformation relative to Lorentz cones, by the natural equation reformulation and the normal equation reformulation, respectively, and establish their local quadratic convergence results under suitable conditions. The convergence analysis shows that the method based on the natural equation formulation is not infl...

New solutions for the elliptic Darboux equation are obtained as particular cases of constructed Heun's general equation. We consider two groups power series expansions and new in Gauss hypergeometric functions. The convergence one group is determined by means ratio tests infinite series, while other designed to solve problems which admit finite-series solutions. Actually, we envisage periodic q...