This paper considers the problem of minimizing a linear function over the intersection of an affine space with a closed convex cone. In the first half of the paper, we give a detailed study of duality properties of this problem and present examples to illustrate these properties. In particular,...

How to initialize an algorithm to solve an optimization problem is of great theoretical and practical importance. In the simplex method for linear programming this issue is resolved by either the two-phase approach or using the so-called big M technique. In the interior point method, there is a...

We propose in this paper an algorithm for solving linearly constrained nondifferentiable convex programming problems. This algorithm combines the ideas of the affine scaling method with the subgradient method. It is a generalization of the dual and interior point method for min-max problems...

We propose a polynomial time primal-dual potential reduction algorithm for linear programming. Unlike any other interior point method, the new algorithm is based on a rank-one updating scheme for sequentially computing the projection matrices. For a standard linear programming problem, the...

How to initialize an algorithm to solve an optimization problem is of great theoretical and practical importance. In the simplex method for linear programming this issue is resolved by either the two-phase approach or using the so-called big M technique. In the interior point method, there is a...

This paper considers the problem of minimizing a linear function over the intersection of an affine space with a closed convex cone. In the first half of the paper, we give a detailed study of duality properties of this problem and present examples to illustrate these properties. In particular,...

We propose in this paper an algorithm for solving linearly constrained nondifferentiable convex programming problems. This algorithm combines the ideas of the affine scaling method with the subgradient method. It is a generalization of the dual and interior point method for min-max problems...

We propose a polynomial time primal-dual potential reduction algorithm for linear programming. Unlike any other interior point method, the new algorithm is based on a rank-one updating scheme for sequentially computing the projection matrices. For a standard linear programming problem, the...