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Hybrid proximal linearized algorithm for the split DC program in infinite-dimensional real Hilbert spaces.

Chih-Sheng Chuang1, Pei-Jung Yang1

  • 1Department of Applied Mathematics, National Chiayi University, Chiayi, Taiwan.

Journal of Inequalities and Applications
|March 7, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a novel hybrid proximal linearized algorithm for split direct current (DC) programs. The algorithm demonstrates convergence in both finite- and infinite-dimensional real Hilbert spaces, advancing optimization theory.

Keywords:
Critical pointDC functionStrongly monotonicitySubdifferential

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Area of Science:

  • Optimization Theory
  • Mathematical Analysis

Background:

  • Existing convergence theorems for DC programs and split DC programs are limited to finite-dimensional spaces.
  • There is a need for algorithms with proven convergence in broader Hilbert space settings.

Purpose of the Study:

  • To develop and analyze a hybrid proximal linearized algorithm for split DC programs.
  • To establish convergence theorems for this algorithm in both finite- and infinite-dimensional real Hilbert spaces.

Main Methods:

  • A hybrid proximal linearized algorithm was designed.
  • Convergence analysis was performed for finite-dimensional real Hilbert spaces.
  • Convergence analysis was performed for infinite-dimensional real Hilbert spaces.

Main Results:

  • The proposed algorithm achieves convergence for split DC programs.
  • Convergence theorems were established for both finite- and infinite-dimensional settings.
  • This extends the applicability of DC programming optimization.

Conclusions:

  • The hybrid proximal linearized algorithm is effective for split DC programs.
  • The study successfully extends convergence guarantees to infinite-dimensional Hilbert spaces.
  • This work provides a robust theoretical foundation for advanced optimization problems.