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Lp Quasi-norm Minimization: Algorithm and Applications.

Omar M Sleem1, M E Ashour2, N S Aybat3

  • 1Department of Electrical Engineering, Pennsylvania State University, State College, PA, 16802 USA.

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Summary
This summary is machine-generated.

This study introduces a novel heuristic method for solving optimization problems by minimizing the Lq-quasi-norm (q<1). The new algorithm offers efficient sparse solutions for various applications, outperforming existing Lq-norm minimization techniques.

Keywords:
ADMMCompressed sensingMatrix completionProximal gradient methodRank minimizationSparsitySystem identification

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Area of Science:

  • Optimization
  • Machine Learning
  • Signal Processing

Background:

  • Sparsity is crucial in statistics, machine learning, and signal processing for efficient computation and storage.
  • Minimizing the Lq-quasi-norm (q<1) is a key objective for achieving sparse solutions in optimization problems.

Approach:

  • A novel iterative two-block algorithm is proposed for Lq-quasi-norm minimization under convex constraints.
  • This method involves solving for polynomial roots, differing from the soft thresholding used in L1-norm minimization.
  • A faster proximal gradient-based algorithm is developed for differentiable convex constraints, enhancing speed and proving convergence.

Key Points:

  • The algorithm effectively handles Lq-quasi-norm minimization with general convex constraints.
  • It offers a computational advantage by avoiding complex thresholding operators.
  • Demonstrated success in sparse signal reconstruction, system identification, and matrix completion.

Conclusions:

  • The proposed heuristic method provides an efficient approach to sparse optimization.
  • The developed algorithms show significant performance gains over existing Lq-quasi-norm minimization techniques.
  • This work advances sparse recovery and related computational fields.