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Coordinate great circle descent algorithm with application to single-index models.

Peng Zeng1, Yichao Wu2

  • 1Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA.

Statistics and Its Interface
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PubMed
Summary
This summary is machine-generated.

We introduce a new coordinate great circle descent algorithm for optimization problems with unit-norm constraints. This method addresses limitations of existing coordinate descent algorithms for non-differentiable and non-separable functions.

Keywords:
Constrained optimizationCoordinate descent algorithmPenalizationSingle-index modelUnit-norm constraint

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Area of Science:

  • Optimization Theory
  • Numerical Analysis

Background:

  • Coordinate descent is effective for high-dimensional, non-differentiable optimization.
  • Existing methods by Tseng (2001) require separable non-differentiable parts.
  • Single index models often involve unit-norm constraints, posing challenges.

Purpose of the Study:

  • To develop a novel algorithm for optimization problems with unit-norm constraints.
  • To address the non-applicability of standard coordinate descent due to constraints and non-separability.
  • To provide theoretical and empirical validation for the proposed method.

Main Methods:

  • Proposal of a coordinate great circle descent algorithm.
  • Theoretical justification of the algorithm's convergence.
  • Simulation studies to assess performance.
  • Application to Boston housing data for single-index model fitting.

Main Results:

  • The coordinate great circle descent algorithm effectively solves the targeted optimization problems.
  • Theoretical analysis confirms the algorithm's validity.
  • Simulation studies demonstrate its practical utility.
  • Successful application in fitting single-index models to real-world data.

Conclusions:

  • The proposed coordinate great circle descent algorithm is a valid and effective method for optimization problems with unit-norm constraints.
  • This work extends the applicability of coordinate descent methods to a broader class of problems.
  • The algorithm shows promise for applications like single-index model fitting.