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Table of Contents
1. Problems Involving Cardinality
2. The L1-Norm Heuristic
3. Convex Relaxation and Convex Envelope Interpretations
4. Examples
5. Recent Results
6. Cardinality
7. General Convex-Cardinality Problems
8. Solving Convex-Cardinality Problems
9. Boolean LP as Convex-Cardinality Problem
10. Sparse Design
11. Sparse Modeling / Regressor Selection
12. Sparse Signal Reconstruction
13. Estimation with Outliers
14. Minimum Number of Violations
15. Linear Classifier with Fewest Errors
16. Smallest Set of Mutually Infeasible Inequalities
17. Portfolio Investment with Linear and Fixed Costs
18. Piecewise Constant Fitting
19. Piecewise Linear Fitting
20. L1-Norm Heuristic
21. Example: Minimum Cardinality Problem
22. Example: Cardinality Constrained Problem
23. Polishing
24. Interpretation as Convex Relaxation
25. Interpretation via Convex Envelope
26. Weighted and Asymmetric L1-Heuristics
27. Regressor Selection
28. Example
29. Sparse Signal Reconstruction
30. Recent Theoretical Results
Summary
This document discusses the application of L1-norm methods for convex-cardinality problems. It covers various aspects such as problems involving cardinality, the L1-norm heuristic, convex relaxation, examples, recent results, cardinality, general convex-cardinality problems, solving techniques, Boolean LP as a convex-cardinality problem, sparse design, regressor selection, signal reconstruction, estimation with outliers, linear classifiers, infeasible inequalities, portfolio investment, piecewise fitting, L1-norm heuristic, interpretation techniques, regressor selection examples, and recent theoretical results.