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<p>This paper delineates a modification of Karmarkar’s projective scaling algorithm, which is represented as a simplified form. The proposed mathematical model provides more computational efficiency for the solution of linear programming problem. The revised algorithm fastens the concept of Karmarkar’s original algorithm with projected scaling approach. This method works with a suitable steepest descent direction and a better step size choice. The computational significance has been discussed by taking numerical experimentation. The complexity of the algorithm as well as rate of convergence has been highlighted.</p>

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Karmarkar’s projective scaling algorithm: an alternative approach

  • 期刊论文

  • 发表日期：

    2026年1月21日

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  • Mitali Madhumita Acharya,
  • Sushree Swetapadma,
  • Sudarsan Nanda,
  • Srikumar Acharya

摘要

This paper delineates a modification of Karmarkar’s projective scaling algorithm, which is represented as a simplified form. The proposed mathematical model provides more computational efficiency for the solution of linear programming problem. The revised algorithm fastens the concept of Karmarkar’s original algorithm with projected scaling approach. This method works with a suitable steepest descent direction and a better step size choice. The computational significance has been discussed by taking numerical experimentation. The complexity of the algorithm as well as rate of convergence has been highlighted.