A Proximal Algorithm with Convergence Guarantee for a Nonconvex Minimization Problem Based on Reproducing Kernel Hilbert Space

The underlying function in reproducing kernel Hilbert space (RKHS) may be degraded by outliers or deviations, resulting in a symmetry ill-posed problem. This paper proposes a nonconvex minimization model with ℓ0-quasi norm based on RKHS to depict this degraded problem. The underlying function in RKH...

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Bibliographic Details
Published in:Symmetry (Basel) 2021-12, Vol.13 (12), p.2393
Main Authors: Dou, Hong-Xia, Deng, Liang-Jian
Format: Article
Language:English
Subjects:
Algorithms
Convergence
convergence analysis
degraded function
Hilbert space
Ill posed problems
Kernels
nonconvex minimization
Optimization
Outliers (statistics)
RKHS
Sequences
Sparsity
symmetry ill-posed problem
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Summary:The underlying function in reproducing kernel Hilbert space (RKHS) may be degraded by outliers or deviations, resulting in a symmetry ill-posed problem. This paper proposes a nonconvex minimization model with ℓ0-quasi norm based on RKHS to depict this degraded problem. The underlying function in RKHS can be represented by the linear combination of reproducing kernels and their coefficients. Thus, we turn to estimate the related coefficients in the nonconvex minimization problem. An efficient algorithm is designed to solve the given nonconvex problem by the mathematical program with equilibrium constraints (MPEC) and proximal-based strategy. We theoretically prove that the sequences generated by the designed algorithm converge to the nonconvex problem’s local optimal solutions. Numerical experiment also demonstrates the effectiveness of the proposed method.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym13122393