110 research outputs found
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Lifted Stationary Points of Sparse Optimization with Complementarity Constraints
We aim to compute lifted stationary points of a sparse optimization problem
(P0) with complementarity constraints. We define a continuous relaxation
problem (Rv) that has the same global minimizers and optimal value with problem
(P0). Problem (Rv) is a mathematical program with complementarity constraints
(MPCC) and a difference-of-convex (DC) objective function. We define MPCC
lifted-stationarity of (Rv) and show that it is weaker than directional
stationarity, but stronger than Clarke stationarity for local optimality.
Moreover, we propose an approximation method to solve (Rv) and an augmented
Lagrangian method to solve its subproblem, which relaxes the equality
constraint in (Rv) with a tolerance. We prove the convergence of our algorithm
to an MPCC lifted-stationary point of problem (Rv) and use a sparse
optimization problem with vertical linear complementarity constraints to
demonstrate the efficiency of our algorithm on finding sparse solutions in
practice.Comment: 29 pages, 3 figure
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