This document proposes a Newton step graph-based model for Quadratic separable Problems (QSP). The Newton step is well suited for this kind of problems, but when the problem size grows the matrix-based QSP model will grow in a non linear manner. Furthermore, handling the constraints becomes the main problem as we have to select the right constraints in the different solution steps. When this ha...

In this paper, we study abelian varieties of dimension 4 over number fields with the property that the Lie algebra of their Mumford–Tate group is C-isomorphic to Ga (sl2)3. Such abelian varieties occur naturally as fibres of universal families of abelian varieties over Shimura curves associated to algebraic groups over Q that are C-isomorphic to (SL2) 3. We study the reductionsmodulo prime idea...

We consider a family of damped quasi-Newton methods for solving unconstrained optimization problems. This family resembles that of Broyden with line searches, except that the change in gradients is replaced by a certain hybrid vector before updating the current Hessian approximation. This damped technique modifies the Hessian approximations so that they are maintained sufficiently positive defi...