A new semidefinite relaxation for \(L_{1}\)-constrained quadratic

DOI10.3934/naco.2015.5.185zbMath1317.90226arXiv1401.0081OpenAlexW2963578791MaRDI QIDQ2353474

Sheng-Nan Han, Yong Xia, Yu-Jun Gong

Publication date: 14 July 2015

Published in: Numerical Algebra, Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.0081

zbMATH Keywords

semidefinite programmingquadratic optimizationsparse principal component analysis\(\ell_1\) unit ball

Mathematics Subject Classification ID

Semidefinite programming (90C22) Quadratic programming (90C20)

Uses Software

• SeDuMi
• CVX

Cites Work

• Convex approximations to sparse PCA via Lagrangian duality
• Pivoting in an outcome polyhedron
• Complexity and nonlinear semidefinite programming reformulation of \(\ell_1\)-constrained nonconvex quadratic optimization
• Improved SDP bounds for minimizing quadratic functions over the \(\ell^{1}\)-ball
• Grothendieck-Type Inequalities in Combinatorial Optimization
• The UGC Hardness Threshold of the L_p Grothendieck Problem
• On semidefinite bounds for maximization of a non-convex quadratic objective over thel₁unit ball
• Cones of Matrices and Set-Functions and 0–1 Optimization
• Local Minimizers of Quadratic Functions on Euclidean Balls and Spheres
• Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
• Trust Region Methods
• New results on semidefinite bounds forℓ₁-constrained nonconvex quadratic optimization
• A Direct Formulation for Sparse PCA Using Semidefinite Programming

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