Primal-dual algorithms have played an integral role in recent developments in approximation algorithms, and yet there has been little work on these algorithms in the context of LP relaxations that have been strengthened by the addition of more sophisticated valid inequalities. We introduce primal-dual schema based on the LP relaxations devised by Carr, Fleischer, Leung & Phillips for the minimu...

Motivated by various applications to computer vision, we consider the convex cost tension problem, which is the dual of the convex cost flow problem. In this paper, we first propose a primal algorithm for computing an optimal solution of the problem. Our primal algorithm iteratively updates primal variables by solving associated minimum cut problems. We show that the time complexity of the prim...

This paper presents estimates of the degree of returns to scale using nonparametric measures of primal and dual productivity for 2-digit US manufacturing industries. As part of the analysis, the cyclical behaviour of primal and dual productivity measures are considered, time-varying markups are allowed for, and the small sample properties of the instrumental variables estimator used to derive t...

In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian, Poisson). On the other hand, as a prior, the images to restore are assumed to be positive and sparsely represented in a dictionary of waveforms. Piecing togethe...

In this paper a symmetric primal-dual transformation for positive semideenite programming is proposed. For standard SDP problems, after this symmetric transformation the primal variables and the dual slacks become identical. In the context of linear programming, existence of such a primal-dual transformation is a well known fact. Based on this symmetric primal-dual transformation we derive Newt...

Motivated by various applications to computer vision, we consider an integer convex optimization problem which is the dual of the convex cost network flow problem. In this paper, we first propose a new primal algorithm for computing an optimal solution of the problem. Our primal algorithm iteratively updates primal variables by solving associated minimum cut problems. The main contribution in t...

In this paper, we present a variant of the primal affine scaling method, which we call the primal power affine scaling method. This method is defined by choosing a real r > 0.5, and is similar to the power barrier variant of the primal-dual homotopy methods considered by den Hertog, Roos and Terlaky and Sheu and Fang. Here, we analyze the methods for r > 1. The analysis for 0.50 < r < 1 is simi...