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<p>This article introduces the concept of geodesic ratio invex functions, extending the framework of invexity to the geodesic setting. Within this context, necessary and sufficient conditions are established for the existence of optimal solutions to multiobjective fractional programming problems. Furthermore, various duality theorems–including weak, strong, and strict converse duality–are developed under geodesic ratio invexity assumptions. Illustrative examples are provided to demonstrate the applicability of the proposed conditions and to validate the established duality relationships.</p>

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Multi-objective fractional programming on Riemannian Manifold

  • 期刊论文

  • 发表日期：

    2026年7月18日

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  • Arindam Panja,
  • Arpita Shome,
  • Rathindra Nath Mukherjee

摘要

This article introduces the concept of geodesic ratio invex functions, extending the framework of invexity to the geodesic setting. Within this context, necessary and sufficient conditions are established for the existence of optimal solutions to multiobjective fractional programming problems. Furthermore, various duality theorems–including weak, strong, and strict converse duality–are developed under geodesic ratio invexity assumptions. Illustrative examples are provided to demonstrate the applicability of the proposed conditions and to validate the established duality relationships.