In this paper we derive effciency estimates of the regularized Newton's method as applied to constrained convex minimization problems and to variational inequalities. We study a one- step Newton's method and its multistep accelerated version, which converges on smooth convex problems as O( 1 k3...

In this paper we propose an accelerated version of the cubic regularization of Newton's method [6]. The original version, used for minimizing a convex function with Lipschitz-continuous Hessian, guarantees a global rate of convergence of order O(1/k exp.2), where k is the iteration counter. Our...

In this paper we derive a lower bound on the average complexity of the Simplex-Method as a solution-process for linear programs (LP) of the type:<Equation ID="Equ1"> <EquationSource Format="TEX"/> </Equation> We assume these problems to be randomly generated according to the Rotation-Symmetry-Model: *Let a <Subscript>1</Subscript>,…,a <Subscript>m</Subscript>, v be distributed independently,...</subscript></subscript></equation>

In this paper we derive a lower bound on the average complexity of the Simplex-Method as a solution-process for linear programs (LP) of the type: We assume these problems to be randomly generated according to the Rotation-Symmetry-Model: *Let a 1 ,…,a m , v be distributed independently,...