The decompositions with respect to two core non-symmetric cones

Yue Lu (), Ching-Yu Yang (), Jein-Shan Chen () and Hou-Duo Qi ()
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Yue Lu: Tianjin Normal University
Ching-Yu Yang: National Taiwan Normal University
Jein-Shan Chen: National Taiwan Normal University
Hou-Duo Qi: University of Southampton

Journal of Global Optimization, 2020, vol. 76, issue 1, No 8, 155-188

Abstract: Abstract It is known that the analysis to tackle with non-symmetric cone optimization is quite different from the way to deal with symmetric cone optimization due to the discrepancy between these types of cones. However, there are still common concepts for both optimization problems, for example, the decomposition with respect to the given cone, smooth and nonsmooth analysis for the associated conic function, conic-convexity, conic-monotonicity and etc. In this paper, motivated by Chares’s thesis (Cones and interior-point algorithms for structured convex optimization involving powers and exponentials, 2009), we consider the decomposition issue of two core non-symmetric cones, in which two types of decomposition formulae will be proposed, one is adapted from the well-known Moreau decomposition theorem and the other follows from geometry properties of the given cones. As a byproduct, we also establish the conic functions of these cones and generalize the power cone case to its high-dimensional counterpart.

Keywords: Moreau decomposition theorem; Power cone; Exponential cone; Non-symmetric cones; 49M27; 90C25 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10898-019-00845-3

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