We previously showed that the solution to the primal problem is equivalent to the solution to the dual problem if they satisfy the following primal-dual equivalence conditions. First, we need a convex objective function and in our case, it is 1 2 ||~ w||2. Second, we need convex inequality constraints gi, which are 1−yi(~ w · ~xi + b) for i = 1, ...,m. The last condition states that for each in...

Our goal in this proposal is to explore the connection between the local ratio technique and linear programming. We believe that a better understanding of this connection will strengthen and extend the local ratio technique and will enable us to apply the technique to a wide variety of problems. Specifically, we intend to improve the best performance guarantee and/or running time of approximati...

We consider finite element discretizations for convection–diffusion problems under low regularity assumptions. The derivation and analysis use the primal–dual weak Galerkin (PDWG) framework. Euler–Lagrange formulation resulting from PDWG scheme yields a system of equations involving not only equation primal variable but also its adjoint dual variable. show that proposed method is stable converg...

We present a first set of results concerning stellar evolution of rotating low-mass stars. Our models include fully consistent transport of angular momentum and chemicals due to the combined action of rotation induced mixing (according to Maeder & Zahn 1998) and element segregation. The analysis of the effects of local variations of molecular weight due to the meridional circulation on the tran...

In this paper, a primal-dual algorithm for total bounded variation (TV)–type image restoration is analyzed and tested. Analytically it turns out that employing a global Lregularization, with 1 < s ≤ 2, in the dual problem results in a local smoothing of the TVregularization term in the primal problem. The local smoothing can alternatively be obtained as the infimal convolution of the r-norm, wi...

Since the theory of ideals plays an important role in the theory of semirings, in this paper we will make an intensive study of the notions of primal and weakly primal ideals in commutative semirings with an identity 1. It is shown that these notions inherit most of the essential properties of the primal and weakly primal ideals of a commutative ring with non-zero identity. Also, the relationsh...

The primal-dual scheme has been used to provide approximation algorithms for many problems. Goemans and Williamson gave a (2−1/(n−1))-approximation for the Prize-Collecting Steiner Tree Problem that runs in O(n3 logn) time—it applies the primaldual scheme once for each of the n vertices of the graph. We present a primal-dual algorithm that runs in O(n2 logn), as it applies this scheme only once...