A primal-dual homotopy algorithm for $$\ell _{1}$$-minimization with $$\ell _{\infty }$$-constraints

A Primal Dual Active Set with Continuation Algorithm for the \ell^0-Regularized Optimization Problem

We develop a primal dual active set with continuation algorithm for solving the l-regularized least-squares problem that frequently arises in compressed sensing. The algorithm couples the the primal dual active set method with a continuation strategy on the regularization parameter. At each inner iteration, it first identifies the active set from both primal and dual variables, and then updates...

A Primal-Dual Homotopy Algorithm for ℓ1-Minimization with ℓ∞-Constraints

In this paper we propose a primal-dual homotopy method for `1minimization problems with infinity norm constraints in the context of sparse reconstruction. The natural homotopy parameter is the value of the bound for the constraints and we show that there exists a piecewise linear solution path with finitely many break points for the primal problem and a respective piecewise constant path for th...

A Primal-Dual Homotopy Algorithm for $\ell_{1}$-Minimization with $\ell_{\infty}$-Constraints

In this paper we propose a primal-dual homotopy method for `1minimization problems with infinity norm constraints in the context of sparse reconstruction. The natural homotopy parameter is the value of the bound for the constraints and we show that there exists a piecewise linear solution path with finitely many break points for the primal problem and a respective piecewise constant path for th...

A $2\ell k$ Kernel for $\ell$-Component Order Connectivity

In the `-Component Order Connectivity problem (` ∈ N), we are given a graph G on n vertices, m edges and a non-negative integer k and asks whether there exists a set of vertices S ⊆ V (G) such that |S| ≤ k and the size of the largest connected component in G−S is at most `. In this paper, we give a kernel for `-Component Order Connectivity with at most 2`k vertices that takes nO(`) time for eve...

A Primal-dual Method for Minimization with Linear Constraints