A globally and linearly convergent PGM for zero-norm regularized quadratic optimization with sphere constraint

Wu Yuqia(935897967qq.com)
Pan Shaohua(shhpanscut.edu.cn)
Bi Shujun(bishjscut.edu.cn)

Abstract: This paper is concerned with the zero-norm regularized quadratic optimization with a sphere constraint, which has an important application in sparse eigenvalue problems. For this class of nonconvex and nonsmooth optimization problems, we establish the KL property of exponent 1/2 for its extended-valued objective function and develop a globally and linearly convergent proximal gradient method (PGM). Numerical experiments are included for sparse principal component analysis (PCA) with synthetic and real data to confirm the obtained theoretic results.

Keywords: KL property of exponent $1/2$; zero-norm; sphere constraint; PGM

Category 1: Nonlinear Optimization (Bound-constrained Optimization )

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Entry Submitted: 11/11/2018
Entry Accepted: 11/11/2018
Entry Last Modified: 11/11/2018

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