The Alternating Direction Method of Multipliers (ADMM) has been proved to be effective for solving separable convex optimization subject to linear constraints. In this paper, we propose a Generalized Symmetric ADMM (GS-ADMM), which updates the Lagrange multiplier twice with suitable stepsizes, to solve the multi-block separable convex programming. This GS-ADMM partitions the data into two group...

We give algorithms for the optimization problem: maxρ 〈Q, ρ〉, where Q is a Hermitian matrix, and the variable ρ is a bipartite separable quantum state. This problem lies at the heart of several problems in quantum computation and information, such as the complexity of QMA(2). While the problem is NPhard, our algorithms are better than brute force for several instances of interest. In particular...

In this paper, we present a technique for designing the optimal (in the mean square error sense) separable 2-D filter for recovering a signal from a noise-corrupted signal when the joint statistics of the signal and noise are known. A set of nonlinear equations in the design parameters is derived, and an iterative algorithm to solve them is presented. The algorithm is shown to be nondivergent i...

We show that with every separable calssical Stäckel system of Benenti type on a Riemannian space one can associate, by a proper deformation of the metric tensor, a multi-parameter family of non-Hamiltonian systems on the same space, sharing the same trajectories and related to the seed system by appropriate reciprocal transformations. These system are known as bi-cofactor systems and are integr...

In this paper, we propose an inexact proximal multiplier method using proximal distances for solving convex minimization problems with a separable structure. The proposed method unified the work of Chen and Teboulle (PCPM method), Kyono and Fukushima (NPCPMM) and Auslender and Teboulle (EPDM) and extends the convergence properties for the class of φ−divergence distances. We prove, under standar...

We study the network coding problem of sum-networks with 3 sources and n terminals (3s/nt sum-network), for an arbitrary positive integer n, and derive a sufficient and necessary condition for the solvability of a family of so-called “terminal-separable” sum-network. Both the condition of “terminal-separable” and the solvability of a terminal-separable sum-network can be decided in polynomial t...

This paper presents a novel image fusion method, suitable for pan-sharpening of multispectral (MS) bands, based on multi-resolution analysis (MRA). The low-resolution MS bands are sharpened by injecting high-pass directional details extracted from the high-resolution panchromatic (Pan) image by means of the curvelet transform, which is a non-separable MRA, whose basis function are directional e...

Introduction This paper describes the application of Newton Method for solving strictly convex separable network quadratic programs. The authors provide a brief synopsis of separable network quadratic programming and list the various techniques for solving the same. The main thrust of the paper is succinctly identified by the following: 1. Providing a generic subroutine that can be used by vari...

This is a talk given at ISMP, Jul 31 2006.

Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics (MD) as a global Monte Carlo move. The acceptance rate of HMC decays exponentially with system size. The shadow hybrid Monte Carlo (SHMC) was previously introduced to reduce this performance degradation by sampling instead from the shadow Hamiltonian defined for MD when using a symplectic integrator. SHMC's perf...