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Vector topical functions and Farkas type theorems with applications

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Abstract

In this paper, some versions of Farkas-type theorems for systems of inequalities consisting of topical functions are established. Vector topical functions are introduced, and Farkas-type theorems for systems involving them are studied as well. It is shown that linear programs with nonnegative coefficients in both objective function and constraints can be transformed to unconstrained concave problems, without adding any extra variables.

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Acknowledgments

The authors are very thankful to the anonymous referee for his valuable comments and useful suggestions. This work has been supported by the Islamic Azad University, Kerman Branch, research project 28677-1390.12.10.

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Authors and Affiliations

  1. Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran

    V. Momenaei Kermani

  2. Department of Applied Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

    A. R. Doagooei

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  1. V. Momenaei Kermani
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  2. A. R. Doagooei
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Correspondence to V. Momenaei Kermani.

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Kermani, V.M., Doagooei, A.R. Vector topical functions and Farkas type theorems with applications. Optim Lett 9, 359–374 (2015). https://doi.org/10.1007/s11590-014-0748-4

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  • DOI: https://doi.org/10.1007/s11590-014-0748-4

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