An Augmented Lagrangian Method for Non-Lipschitz Nonconvex Programming
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Publication:2957850
DOI10.1137/15M1052834zbMath1421.90119OpenAlexW2579964591MaRDI QIDQ2957850
Xiaojun Chen, Lei Guo, Zhaosong Lu, Jane J. Ye
Publication date: 30 January 2017
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/15m1052834
Nonconvex programming, global optimization (90C26) Nonlinear programming (90C30) Approximation methods and heuristics in mathematical programming (90C59)
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Cites Work
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- A smoothing SQP framework for a class of composite \(L_q\) minimization over polyhedron
- Iterative hard thresholding methods for \(l_0\) regularized convex cone programming
- New results on constraint qualifications for nonlinear extremum problems and extensions
- An adaptive augmented Lagrangian method for large-scale constrained optimization
- A note on the complexity of \(L _{p }\) minimization
- A relaxed constant positive linear dependence constraint qualification and applications
- An augmented Lagrangian approach for sparse principal component analysis
- Iterative thresholding for sparse approximations
- Complexity analysis of interior point algorithms for non-Lipschitz and nonconvex minimization
- Lower Bound Theory of Nonzero Entries in Solutions of $\ell_2$-$\ell_p$ Minimization
- Sparse and stable Markowitz portfolios
- A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms
- Optimization Methods in Finance
- Linearly Constrained Non-Lipschitz Optimization for Image Restoration
- From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
- Two-Point Step Size Gradient Methods
- Atomic Decomposition by Basis Pursuit
- Variational Analysis
- Necessary conditions for constrained optimization problems with semicontinuous and continuous data
- Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
- Sparse Reconstruction by Separable Approximation
- Joint Power and Admission Control: Non-Convex <formula formulatype="inline"><tex Notation="TeX">$L_{q}$</tex></formula> Approximation and An Effective Polynomial Time Deflation Approach
- Efficient Reconstruction of Piecewise Constant Images Using Nonsmooth Nonconvex Minimization
- Penalty Methods for a Class of Non-Lipschitz Optimization Problems
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