In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...

The clinically reported case of liver involvement with multiple myeloma (MM) is rare. Amyloidosis, defined as a tissue deposition of clonal light-chain fibrils, has been reported in 10-15% of the MM patients. We described a rare MM patient with the primal presentation of fulminant hepatic failure and biliary system involvement due to amyloidosis. Our patient had the primal symptoms of hyperbili...

We present new primal-dual algorithms for several network design problems. The problems considered are the generalized Steiner tree problem (GST), the directed Steiner tree problem (DST), and the set cover problem (SC) which is a subcase of DST. All our problems are NP-hard; so we are interested in approximation algorithms for them. First we give an algorithm for DST which is based on the tradi...

We consider the separable nonlinear and strictly convex single-commodity network flow problem (SSCNFP). We develop a computational scheme for generating a primal feasible solution from any Lagrangian dual vector; this is referred to as “early primal recovery”. It is motivated by the desire to obtain a primal feasible vector before convergence of a Lagrangian scheme; such a vector is not availab...

We introduce an analysis framework for constructing optimal first-order primal-dual methods for the prototypical constrained convex optimization template. While this class of methods offers scalability advantages in obtaining numerical solutions, they have the disadvantage of producing sequences that are only approximately feasible to the problem constraints. As a result, it is theoretically ch...

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...

In this paper, we propose a new primal-dual algorithm for minimizing f(x) + g(x) + h(Ax), where f , g, and h are convex functions, f is differentiable with a Lipschitz continuous gradient, and A is a bounded linear operator. It has some famous primal-dual algorithms for minimizing the sum of two functions as special cases. For example, it reduces to the Chambolle-Pock algorithm when f = 0 and a...

We analyze the multiple cut generation scheme in the analytic center cutting plane method. We propose an optimal primal and dual updating direction when the cuts are central. The direction is optimal in the sense that it maximizes the product of the new dual slacks and of the new primal variables within the trust regions defined by Dikin’s primal and dual ellipsoids. The new primal and dual dir...

In this paper, we present a simple and modularized neural network architecture, named primal-dual group convolutional neural networks (PDGCNets). The main point lies in a novel building block, a pair of two successive group convolutions: primal group convolution and dual group convolution. The two group convolutions are complementary: (i) the convolution on each primal partition in primal group...

in this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual interior point method (ipm) based on a new kernel function with a trigonometric barrier term. iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. although our proposed kernel function is neither a self-regular (sr) function nor logarithmic barrier ...