The H-differentiability and calmness of circular cone functions

Jinchuan Zhou; Yu Lin Chang; Jein Shan Chen

doi:10.1007/s10898-015-0312-5

The H-differentiability and calmness of circular cone functions

Jinchuan Zhou, Yu Lin Chang, Jein Shan Chen^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Let (Formula presented.) be the circular cone in (Formula presented.) which includes second-order cone as a special case. For any function f from (Formula presented.), one can define a corresponding vector-valued function (Formula presented.) on v by applying f to the spectral values of the spectral decomposition of (Formula presented.) with respect to (Formula presented.). The main results of this paper are regarding the H-differentiability and calmness of circular cone function (Formula presented.). Specifically, we investigate the relations of H-differentiability and calmness between f and (Formula presented.). In addition, we propose a merit function approach for solving the circular cone complementarity problems under H-differentiability. These results are crucial to subsequent study regarding various analysis towards optimizations associated with circular cone.

Original language	English
Pages (from-to)	811-833
Number of pages	23
Journal	Journal of Global Optimization
Volume	63
Issue number	4
DOIs	https://doi.org/10.1007/s10898-015-0312-5
Publication status	Published - 2015 Dec 1

Keywords

Calmness
Circular cone
H-differentiable

ASJC Scopus subject areas

Computer Science Applications
Management Science and Operations Research
Control and Optimization
Applied Mathematics

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10.1007/s10898-015-0312-5

Cite this

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title = "The H-differentiability and calmness of circular cone functions",

abstract = "Let (Formula presented.) be the circular cone in (Formula presented.) which includes second-order cone as a special case. For any function f from (Formula presented.), one can define a corresponding vector-valued function (Formula presented.) on v by applying f to the spectral values of the spectral decomposition of (Formula presented.) with respect to (Formula presented.). The main results of this paper are regarding the H-differentiability and calmness of circular cone function (Formula presented.). Specifically, we investigate the relations of H-differentiability and calmness between f and (Formula presented.). In addition, we propose a merit function approach for solving the circular cone complementarity problems under H-differentiability. These results are crucial to subsequent study regarding various analysis towards optimizations associated with circular cone.",

keywords = "Calmness, Circular cone, H-differentiable",

author = "Jinchuan Zhou and Chang, {Yu Lin} and Chen, {Jein Shan}",

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T1 - The H-differentiability and calmness of circular cone functions

AU - Zhou, Jinchuan

AU - Chang, Yu Lin

AU - Chen, Jein Shan

PY - 2015/12/1

Y1 - 2015/12/1

N2 - Let (Formula presented.) be the circular cone in (Formula presented.) which includes second-order cone as a special case. For any function f from (Formula presented.), one can define a corresponding vector-valued function (Formula presented.) on v by applying f to the spectral values of the spectral decomposition of (Formula presented.) with respect to (Formula presented.). The main results of this paper are regarding the H-differentiability and calmness of circular cone function (Formula presented.). Specifically, we investigate the relations of H-differentiability and calmness between f and (Formula presented.). In addition, we propose a merit function approach for solving the circular cone complementarity problems under H-differentiability. These results are crucial to subsequent study regarding various analysis towards optimizations associated with circular cone.

AB - Let (Formula presented.) be the circular cone in (Formula presented.) which includes second-order cone as a special case. For any function f from (Formula presented.), one can define a corresponding vector-valued function (Formula presented.) on v by applying f to the spectral values of the spectral decomposition of (Formula presented.) with respect to (Formula presented.). The main results of this paper are regarding the H-differentiability and calmness of circular cone function (Formula presented.). Specifically, we investigate the relations of H-differentiability and calmness between f and (Formula presented.). In addition, we propose a merit function approach for solving the circular cone complementarity problems under H-differentiability. These results are crucial to subsequent study regarding various analysis towards optimizations associated with circular cone.

KW - Calmness

KW - Circular cone

KW - H-differentiable

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The H-differentiability and calmness of circular cone functions

Abstract

Keywords

ASJC Scopus subject areas

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