Differential properties of Euclidean projection onto power cone

Le Hien ()

Mathematical Methods of Operations Research, 2015, vol. 82, issue 3, 265-284

Abstract: In this paper, we study differential properties of Euclidean projection onto the high dimensional power cone $$\begin{aligned} K^{\alpha }_{m,n}=\left\{ (x,z)\in \mathbb {R}^m_+ \times \mathbb {R}^n, \left| \left| {z} \right| \right| \le \prod \nolimits _{i=1}^m x_i^{\alpha _i}\right\} , \end{aligned}$$ K m , n α = ( x , z ) ∈ R + m × R n , z ≤ ∏ i = 1 m x i α i , where $$0>\alpha _i, \sum \nolimits _{i=1}^m \alpha _i=1$$ 0 > α i , ∑ i = 1 m α i = 1 . Projector’s formulas, its directional derivative formulas, its first order Fréchet derivative formulas are considered. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Power cone; Euclidean projection; Differential properties (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s00186-015-0514-0

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