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A Geometric Mean of Parameterized Arithmetic and Harmonic Means of Convex Functions

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  • Sangho Kum
  • Yongdo Lim

Abstract

The notion of the geometric mean of two positive reals is extended by Ando (1978) to the case of positive semidefinite matrices A and B. Moreover, an interesting generalization of the geometric mean A # B of A and B to convex functions was introduced by Atteia and Raïssouli (2001) with a different viewpoint of convex analysis. The present work aims at providing a further development of the geometric mean of convex functions due to Atteia and Raïssouli (2001). A new algorithmic self‐dual operator for convex functions named “the geometric mean of parameterized arithmetic and harmonic means of convex functions” is proposed, and its essential properties are investigated.

Suggested Citation

  • Sangho Kum & Yongdo Lim, 2012. "A Geometric Mean of Parameterized Arithmetic and Harmonic Means of Convex Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:836804
    DOI: 10.1155/2012/836804
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    References listed on IDEAS

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    1. Yu. E. Nesterov & M. J. Todd, 1997. "Self-Scaled Barriers and Interior-Point Methods for Convex Programming," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 1-42, February.
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