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Pseudoconvexity on a closed convex set: an application to a wide class of generalized fractional functions

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  • Laura Carosi

    (University of Pisa)

Abstract

The issue of the pseudoconvexity of a function on a closed set is addressed. It is proved that if a function has no critical points on the boundary of a convex set, then the pseudoconvexity on the interior guarantees the pseudoconvexity on the closure of the set. This result holds even when the boundary of the set contains line segments, and it is used to characterize the pseudoconvexity, on the nonnegative orthant, of a wide class of generalized fractional functions, namely the sum between a linear one and a ratio which has an affine function as numerator and, as denominator, the p-th power of an affine function. The relationship between quasiconvexity and pseudoconvexity is also investigated.

Suggested Citation

  • Laura Carosi, 2017. "Pseudoconvexity on a closed convex set: an application to a wide class of generalized fractional functions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 145-158, November.
    • Handle: RePEc:spr:decfin:v:40:y:2017:i:1:d:10.1007_s10203-017-0185-9
    DOI: 10.1007/s10203-017-0185-9
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    References listed on IDEAS

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    1. Cambini, Riccardo & Sodini, Claudio, 2010. "A unifying approach to solve some classes of rank-three multiplicative and fractional programs involving linear functions," European Journal of Operational Research, Elsevier, vol. 207(1), pages 25-29, November.
    2. Laura Carosi & Laura Martein, 2013. "Characterizing the pseudoconvexity of a wide class of generalized fractional functions," Discussion Papers 2013/172, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    3. Laura Carosi & Laura Martein, 2008. "A sequential method for a class of pseudoconcave fractional problems," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 153-164, June.
    4. Alberto Cambini & Laura Martein, 2009. "Generalized Convexity and Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-70876-6, December.
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    More about this item

    Keywords

    Pseudoconvexity; Quasiconvexity; Fractional programming;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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