In this paper we will discuss two variants of an inexact feasible interior point algorithm for convex quadratic programming. We will consider two different neighbourhoods: a (small) one induced by the use of the Euclidean norm which yields a short-step algorithm and a symmetric one induced by the use of the infinity norm which yields a (practical) long-step algorithm. Both algorithms allow for ...

We present a new full Nesterov and Todd step infeasible interior-point algorithm for semi-definite optimization. The algorithm decreases the duality gap and the feasibility residuals at the same rate. In the algorithm, we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Every main iteration of the algorithm consists of a feasibility...

Received: March 10, 2011 Accepted: April 8, 2011 doi:10.5539/jmr.v3n3p159 Abstract This paper presents an alternative technique for solving linear programming problems. It is centered on finding a feasible interior point each time the feasible region is contracted, thus generating a sequence of feasible interior points that converge at the optimal solution of linear programming problem. The con...

The feasible region of this LP is in general, a convex polyhedron. Visualize it as a polygon in 2 dimensions, for simplicity. Now, maximizing yT b is the same as maximizing the projection of the vector y in the direction represented by vector b. For whichever direction b we choose, the point y that maximizes yT b cannot lie strictly in the interior of the feasible region. The reason is that, fr...

Optimization problems with second-order cone constraints SOCs can be solved efficiently by interior point methods. In order for some of these methods to get started or to converge faster, it is important to have an initial feasible point or near-feasible point. In this paper, we study and apply Chinneck’sOriginal constraint consensus method andDBmax constraint consensus method to find near-feas...

We propose an infeasible interior proximal method for solving variational inequality problems with maximal monotone operators and linear constraints. The interior proximal method proposed by Auslender, Teboulle and Ben-Tiba [3] is a proximal method using a distance-like barrier function and it has a global convergence property under mild assumptions. However, this method is applicable only to p...