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Minimization Problems on Strictly Convex Divergences

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  • Nishiyama, Tomohiro

Abstract

The divergence minimization problem plays an important role in various fields. In this note, we focus on differentiable and strictly convex divergences. For some minimization problems, we show the minimizer conditions and the uniqueness of the minimizer without assuming a specific form of divergences. Furthermore, we show geometric properties related to the minimization problems.

Suggested Citation

  • Nishiyama, Tomohiro, 2020. "Minimization Problems on Strictly Convex Divergences," OSF Preprints wzayx, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:wzayx
    DOI: 10.31219/osf.io/wzayx
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    References listed on IDEAS

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    1. Nishiyama, Tomohiro, 2019. "Monotonically Decreasing Sequence of Divergences," OSF Preprints wr2s6, Center for Open Science.
    2. Thomas Breuer & Imre Csiszár, 2016. "Measuring Distribution Model Risk," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 395-411, April.
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    Cited by:

    1. Nishiyama, Tomohiro, 2020. "Convex Optimization on Functionals of Probability Densities," OSF Preprints 8nzum, Center for Open Science.

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