The final goal of this paper is to introduce certain finite dimensional Hopf algebras associated with restricted Frobenius Lie algebras over a field of characteristic p > 0. The antipodes of these Hopf algebras have order either 2p or 2, and in the minimal dimension p there exists just one Hopf algebra in this class which coincides with an example due to Radford [35] of a Hopf algebra with a no...

Here we present a primal-dual interior point multidimensional filter line search method for nonlinear programming. The filter relies on a multidimensional feasibility measure enforcing every constraint violation to zero. To prevent convergence to feasible nonoptimal points a sufficient reduction criterion is also imposed on the barrier function. The evaluation of the method is until now made on...

In [H. Mansouri and C. Roos, Numer. Algorithms 52 (2009) 225-255.], Mansouri and Ross presented a primal-dual infeasible interior-point algorithm with full-Newton steps whose iteration bound coincides with the best known bound for infeasible interior-point methods. Here, we introduce a slightly different algorithm with a different search direction and show that the same complexity result is obt...

The starting point used by an interior point algorithm for linear and convex quadratic programming may significantly influence the behaviour of the method. A widely used heuristic to construct such a point consists of dropping variable nonnegativity constraints and computing a solution which minimizes the Euclidean norm of the primal (or dual) point while satisfying the appropriate primal (or d...

Amenability of any of the algebras described in the title is known to force them to be finite-dimensional. The analogous problems for approximate amenability have been open for some years now. In this article we give a complete solution for the first two classes, using a new criterion for showing that certain Banach algebras without bounded approximate identities cannot be approximately amenabl...

A novel primal-dual path-following interior-point algorithm for the Cartesian P∗(κ)-linear complementarity problem over symmetric cones is presented. The algorithm is based on a reformulation of the central path for finding the search directions. For a full Nesterov-Todd step feasible interior-point algorithm based on the new search directions, the complexity bound of the algorithm with small-u...

We propose a unified framework for the update of the barrier parameter in interior-point methods for nonlinear programming. The original primal-dual system is augmented to incorporate explicitly an updating function. We analyze local convergence properties and recover known updating strategies as special cases. We report numerical experiments on nonlinear problems and compare our results to a s...

In this paper, a new weighted short-step primal-dual interior point algorithm for convex quadratic optimization (CQO) problems is presented. The algorithm uses at each interior point iteration only full-Newton steps and the strategy of the central path to obtain an ε-approximate solution of CQO. This algorithm yields the best currently wellknown theoretical iteration bound, namely, O( √ n log ε...

Interior-point methods possess strong theoretical properties and have been successfully applied to a wide variety of linear and nonlinear programming applications. This paper presents a class of algorithms, based on interior-point methodology, for performing regularized maximum likelihood reconstructions on 3-D emission tomography data. The algorithms solve a sequence of subproblems that conver...

In this paper we deal with regularity conditions, formulated by making use of the quasirelative interior and/or of the quasi interior of the sets involved, which guarantee strong duality for a convex optimization problem with cone (and equality) constraints and its Lagrange dual. We discuss also some results recently on this topic, which are proved to have either superfluous or contradictory as...