The first-order necessary conditions for sparsity constrained optimization

DOI10.1007/s40305-015-0107-xzbMath1332.90209OpenAlexW2189653089MaRDI QIDQ259127

Xue Li, Wen Song

Publication date: 11 March 2016

Published in: Journal of the Operations Research Society of China (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40305-015-0107-x

zbMATH Keywords

first-order necessary conditionssparsity constrained optimizationMordukhovich normal cone

Mathematics Subject Classification ID

Applications of mathematical programming (90C90) Nonconvex programming, global optimization (90C26) Optimality conditions and duality in mathematical programming (90C46)

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Cites Work

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• On solutions of sparsity constrained optimization
• Restricted normal cones and sparsity optimization with affine constraints
• Lipschitzian stability of parametric variational inequalities over generalized polyhedra in Banach spaces
• Honest variable selection in linear and logistic regression models via \(\ell _{1}\) and \(\ell _{1}+\ell _{2}\) penalization
• Optimality conditions for disjunctive optimization in reflexive Banach spaces
• High-dimensional generalized linear models and the lasso
• Optimality conditions for disjunctive programs with application to mathematical programs with equilibrium constraints
• On the Minimization Over Sparse Symmetric Sets: Projections, Optimality Conditions, and Algorithms
• Sparsity Constrained Nonlinear Optimization: Optimality Conditions and Algorithms
• Compressed Sensing With Nonlinear Observations and Related Nonlinear Optimization Problems
• Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
• Variational Analysis
• Greedy Sparsity-Constrained Optimization
• Sparse Approximation via Penalty Decomposition Methods
• On calculating the normal cone to a finite union of convex polyhedra†
• For most large underdetermined systems of linear equations the minimal 𝓁₁‐norm solution is also the sparsest solution