A First-Order Smoothed Penalty Method for Compressed Sensing

We propose a first-order smoothed penalty algorithm (SPA) to solve the sparse recovery problem min{||x||_1 : Ax=b}. SPA is efficient as long as the matrix-vector product Ax and A^Ty can be computed efficiently; in particular, A need not be an orthogonal projection matrix. SPA converges to the target signal by solving a sequence of penalized … Read more

Approximating semidefinite packing problems

In this paper we define semidefinite packing programs and describe an algorithm to approximately solve these problems. Semidefinite packing programs arise in many applications such as semidefinite programming relaxations for combinatorial optimization problems, sparse principal component analysis, and sparse variance unfolding technique for dimension reduction. Our algorithm exploits the structural similarity between semidefinite packing programs … Read more

Real-Time Optimization as a Generalized Equation

We establish results for the problem of tracking a time-dependent manifold arising in online nonlinear programming by casting this as a generalized equation. We demonstrate that if points along a solution manifold are consistently strongly regular, it is possible to track the manifold approximately by solving a linear complementarity problem (LCP) at each time step. … Read more

Lifting Group Inequalities and an Application to Mixing Inequalities

Given a valid inequality for the mixed integer infinite group relaxation, a lifting based approach is presented that can be used to strengthen this inequality. Bounds on the solution of the corresponding lifting problem and some necessary conditions for the lifted inequality to be minimal for the mixed integer infinite group relaxation are presented. Finally, … Read more

Convergence of fixed-point continuation algorithms for matrix rank minimization

The matrix rank minimization problem has applications in many fields such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization problem, is often solved instead. Recently, Ma, Goldfarb and Chen proposed a fixed-point continuation algorithm for solving the nuclear norm minimization problem. … Read more

Starting-Point Strategies for an Infeasible Potential Reduction Method

We present two strategies for choosing a “hot” starting-point in the context of an infeasible Potential Reduction (PR) method for convex Quadratic Programming. The basic idea of both strategies is to select a preliminary point and to suitably scale it in order to obtain a starting point such that its nonnegative entries are sufficiently bounded … Read more

Stability for solution of Differential Variational Inequalitiy

In this paper we study the class of differential variational inequality(DVI) in a finite-dimension Euclidean space. We study stability and perturbation of the DVI under the OSL condition. Besides, we establish a Prior Bound Theorem, which is a useful tool to prove stability of DVI. In this paper, we replace the classical Lipshitz continuity by … Read more

Rank-Sparsity Incoherence for Matrix Decomposition

Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of applications in model and system identification, and is NP-hard in general. In this … Read more

An inexact parallel splitting augmented Lagrangian method for large system of linear equations

Parallel iterative methods are power tool for solving large system of linear equations (LQs). The existing parallel computing research results are all most concentred to sparse system or others particular structure, and all most based on parallel implementing the classical relaxation methods such as Gauss-Seidel, SOR, and AOR methods e±ciently on multiprcessor systems. In this … Read more

Interior Proximal Algorithm with Variable Metric for Second-Order Cone Programming: Applications to Structural Optimization and Support Vector Machines

In this work, we propose an inexact interior proximal type algorithm for solving convex second-order cone programs. This kind of problems consists of minimizing a convex function (possibly nonsmooth) over the intersection of an affine linear space with the Cartesian product of second-order cones. The proposed algorithm uses a distance variable metric, which is induced … Read more