Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems

Nikos Komodakis just sent the following:

Dear Igor,

Jean-Christophe Pesquet and I have recently finished a tutorial paper entitled "Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems",  which is going to appear as a feature article in an upcoming issue of the highly selective IEEE Signal Processing magazine.

The main goals of the above paper are:
- To provide a thorough introduction that intuitively explains the basic principles and ideas behind primal-dual approaches, including detailing useful connections between primal-dual methods and some widely used optimization techniques like the alternating direction method of multipliers (ADMM).
- To describe how these methods can be employed both in the context of continuous optimization and in the context of discrete optimization.
- To explain some of the recent advances that have taken place concerning primal-dual algorithms for solving large-scale optimization problems.
- And to also provide examples of useful applications in the context of image analysis and signal processing.

The uploaded version of the paper to arxiv can be found here: http://arxiv.org/abs/1406.5429

We believe that this could be of interest to the readers of your blog. If you also feel that this is case, we would be really glad if you could post some relevant information in your blog.

Best regards,
Nikos Komodakis

Thanks Nikos. here is the review:

Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems by Nikos Komodakis, Jean-Christophe Pesquet

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. Deriving efficient strategies which jointly brings into play the primal and the dual problems is however a more recent idea which has generated many important new contributions in the last years. These novel developments are grounded on recent advances in convex analysis, discrete optimization, parallel processing, and non-smooth optimization with emphasis on sparsity issues. In this paper, we aim at presenting the principles of primal-dual approaches, while giving an overview of numerical methods which have been proposed in different contexts. We show the benefits which can be drawn from primal-dual algorithms both for solving large-scale convex optimization problems and discrete ones, and we provide various application examples to illustrate their usefulness.  

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