345. Relaxation Approaches for Nonlinear Sparse Optimization Problems
Invited abstract in session WE-6: Higher-order Methods in Mathematical Programming I, stream Challenges in nonlinear programming.
Wednesday, 14:10 - 15:50Room: M:H
Authors (first author is the speaker)
| 1. | Steffensen Sonja
|
| RWTH Aachen University |
Abstract
In many applications, sparse solutions are favoured over non-sparse solutions with comparable objective value. One approach to induce sparsity relies on the $\ell_0$ norm in the objective. Often this semicontinuous function is approximated using the continuous and convex $\ell_1$-norm instead. However, this approximation can lead to suboptimal results with respect to the sparsity of the solution. We will present alternative exact reformulations (with respect to the $\ell_0$ norm) and relaxations leading to standard nonlinear but nonconvex programs. In our talk we will discuss and relate the relations between the different reformulations in particular with respect to the original problem. Furthermore, we accompany the theoretical results by some numerical tests using randomly generated data sets and give a brief outlook on the application of our approach to sparse optimal control problems.
Keywords
- Complementarity and variational problems
Status: accepted
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