Constructions of complementarity functions and merit functions for circular cone complementarity problem

Miao, Xin-He; Guo, Shengjuan; Qi, Nuo; Chen, Jein Shan

doi:10.1007/s10589-015-9781-1

Cited by 11 publications

(4 citation statements)

References 15 publications

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“…The above results further enrich those given in [4] and [19]; for example, a merit function associated with FB function is given and the case of M being invertible is also considered.…”

Section: Theorem 53 Suppose F and G Are H -Differentiable And The H supporting

confidence: 70%

“…Taking limsup on both sides of (19) and using the fact that > 0 can be sufficiently small, it follows that f L θ is calm at x with the upper bound of cam( f L θ )(x) given as in (16).…”

Section: Calmnessmentioning

confidence: 99%

“…The CCCP is introduced in [19], where some merit functions related with natural residual (NR) functions are presented. Here we study the merit function associated with the Fisher-Burmeister (FB) complementarity function.…”

Section: Cccp Under H-differentiabilitymentioning

confidence: 99%

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The H-differentiability and calmness of circular cone functions

2015

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Let L θ be the circular cone in R n which includes second-order cone as a special case. For any function f from R to R, one can define a corresponding vector-valued function f L θ on R n by applying f to the spectral values of the spectral decomposition of x ∈ R n with respect to L θ . The main results of this paper are regarding the H -differentiability and calmness of circular cone function f L θ . Specifically, we investigate the relations of H -differentiability and calmness between f and f L θ . 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.

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“…The above results further enrich those given in [4] and [19]; for example, a merit function associated with FB function is given and the case of M being invertible is also considered.…”

Section: Theorem 53 Suppose F and G Are H -Differentiable And The H supporting

confidence: 70%

“…Taking limsup on both sides of (19) and using the fact that > 0 can be sufficiently small, it follows that f L θ is calm at x with the upper bound of cam( f L θ )(x) given as in (16).…”

Section: Calmnessmentioning

confidence: 99%

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The H-differentiability and calmness of circular cone functions

2015

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“…Bai et al [3] developed a primal-dual kernel function-based IPM for CO. Zhou et al [29] and Chi et al [4] studied the variational analysis of CO and circular cone eigenvalue complementarity problems (CCECP), respectively. Miao et al [18] considered the constructions of complementarity functions and merit functions for CCCP.…”

Section: Behrouz Kheirfam and Guoqiang Wangmentioning

confidence: 99%

An infeasible full NT-step interior point method for circular optimization

Kheirfam¹,

Wang²

2017

Numerical Algebra, Control &Amp; Optimization

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In this paper, we design a primal-dual infeasible interior-point method for circular optimization that uses only full Nesterov-Todd steps. Each main iteration of the algorithm consisted of one so-called feasibility step. Furthermore, giving a complexity analysis of the algorithm, we derive the currently best-known iteration bound for infeasible interior-point methods.2010 Mathematics Subject Classification. 90C51.

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Smoothing inexact Newton method based on a new derivative-free nonmonotone line search for the NCP over circular cones

Tang

Zhou

2020

Ann Oper Res

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Constructions of complementarity functions and merit functions for circular cone complementarity problem

Cited by 11 publications

References 15 publications

The H-differentiability and calmness of circular cone functions

The H-differentiability and calmness of circular cone functions

An infeasible full NT-step interior point method for circular optimization

Smoothing inexact Newton method based on a new derivative-free nonmonotone line search for the NCP over circular cones

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