TY - JOUR
T1 - The decompositions with respect to two core non-symmetric cones
AU - Lu, Yue
AU - Yang, Ching Yu
AU - Chen, Jein Shan
AU - Qi, Hou Duo
N1 - Funding Information:
The first author?s work is supported by National Natural Science Foundation of China (Grant Number 11601389) and Doctoral Foundation of Tianjin Normal University (Grant Number 52XB1513). The third author?s work is supported by Ministry of Science and Technology, Taiwan.
Funding Information:
The first author’s work is supported by National Natural Science Foundation of China (Grant Number 11601389) and Doctoral Foundation of Tianjin Normal University (Grant Number 52XB1513). The third author’s work is supported by Ministry of Science and Technology, Taiwan.
Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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.
AB - 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.
KW - Exponential cone
KW - Moreau decomposition theorem
KW - Non-symmetric cones
KW - Power cone
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U2 - 10.1007/s10898-019-00845-3
DO - 10.1007/s10898-019-00845-3
M3 - Article
AN - SCOPUS:85076521637
VL - 76
SP - 155
EP - 188
JO - Journal of Global Optimization
JF - Journal of Global Optimization
SN - 0925-5001
IS - 1
ER -