Positive Solutions of Real Homogeneous Algebraic Inequalities

  • Alexander Shananin
  • Sergey TarasovEmail author
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 133)


We show a simple and explicit reduction of the problem of the existence of positive solution of a system of real algebraic homogeneous inequalities in \( R_{ + }^{n} \) to solvability of a standard concave programming problem, which in turn is equivalent to checking whether a particular constraint of a finite system of convex inequalities is redundant. We illustrate this result on two well-known problems in mathematical economics: the weak separability problem and the collective consumption behavior for the homogeneous utilities.


Convexity Redundant constraint Posinomials Utility function Economic indices theory Collective axiom of revealed preference Weak separability property 



The first author is partially supported by Russian Foundation for Basic Research, project No. 17-51-150001. The second author is partially supported by Russian Foundation for Basic Research, project No. 17-0700300.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Moscow Institute of Physics and Technology (MIPT)Dolgoprudny, Moscow RegionRussian Federation

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