... In this paper, we survey the various theoretical and practical issues related to degeneracy in IPM's for linear programming. We survey results which for the most part already appeared in the literature. Roughly speaking, we shall deal with four topics: the effect of degeneracy on the convergence of IPM's, on the trajectories followed by the algorithms, the effect of degeneracy in numerical performance, and on finding basic solutions.

We introduce Greedy Basis Pursuit (GBP), a new algorithm for computing signal representations using overcomplete dictionaries. GBP is rooted in computational geometry and exploits an equivalence between minimizing the ℓ 1-norm of the representation coefficients and determining the intersection of the signal with the convex hull of the dictionary. GBP unifies the different advantages of previous algorithms: like standard approaches to Basis Pursuit, GBP computes representations that have minimum ℓ 1-norm; like greedy algorithms such as Matching Pursuit, GBP builds up representations, sequentially selecting atoms. We describe the algorithm, demonstrate its performance, and provide code. Experiments show that GBP can provide a fast alternative to standard linear programming approaches to Basis Pursuit.

this paper, we survey the various theoretical and practical issues related to degeneracy in IPM's for linear programming. We survey results which for the most part already appeared in the literature. Roughly speaking, we shall deal with four topics: the effect of degeneracy on the convergence of IPM's, on the trajectories followed by the algorithms, the effect of degeneracy in numerical performance, and on finding basic solutions. Key words: Linear programming, interior point methods, degeneracy, polynomial algorithms, global and local convergence, basis recovery, numerical performance, sensitivity analysis. 1 Introduction

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Abstract not found