Lagrangian duality and saddle points for sparse linear programming

[1]  Sebastian Link,et al.  Embedded Cardinality Constraints , 2018, CAiSE.

[2]  Alexandra Schwartz,et al.  Second-Order Optimality Conditions and Improved Convergence Results for Regularization Methods for Cardinality-Constrained Optimization Problems , 2018, J. Optim. Theory Appl..

[3]  J. Pang,et al.  On the Finite Number of Directional Stationary Values of Piecewise Programs , 2018, 1803.00190.

[4]  Ran Dai,et al.  Weighted Network Design With Cardinality Constraints via Alternating Direction Method of Multipliers , 2018, IEEE Transactions on Control of Network Systems.

[5]  Naihua Xiu,et al.  Restricted Robinson Constraint Qualification and Optimality for Cardinality-Constrained Cone Programming , 2017, J. Optim. Theory Appl..

[6]  Naihua Xiu,et al.  Optimality conditions for sparse nonlinear programming , 2017 .

[7]  Xiaojun Chen,et al.  Sparse solutions of linear complementarity problems , 2016, Mathematical programming.

[8]  Shabbir Ahmed,et al.  Exact augmented Lagrangian duality for mixed integer linear programming , 2016, Mathematical Programming.

[9]  Marcel Mongeau,et al.  Exact Sparse Approximation Problems via Mixed-Integer Programming: Formulations and Computational Performance , 2016, IEEE Transactions on Signal Processing.

[10]  Nadav Hallak,et al.  On the Minimization Over Sparse Symmetric Sets: Projections, Optimality Conditions, and Algorithms , 2016, Math. Oper. Res..

[11]  Xue Li,et al.  The First-Order Necessary Conditions for Sparsity Constrained Optimization , 2015 .

[12]  Naihua Xiu,et al.  On Solutions of Sparsity Constrained Optimization , 2015 .

[13]  D. Bertsimas,et al.  Best Subset Selection via a Modern Optimization Lens , 2015, 1507.03133.

[14]  Chao Zhang,et al.  Minimal Zero Norm Solutions of Linear Complementarity Problems , 2014, J. Optim. Theory Appl..

[15]  Stephen C. Graves,et al.  Sparsity-Constrained Transportation Problem , 2014, 1402.2309.

[16]  Boris S. Mordukhovich,et al.  An Easy Path to Convex Analysis and Applications , 2013, Synthesis Lectures on Mathematics & Statistics.

[17]  S. Scholtes.  Introduction to Piecewise Differentiable Equations , 2012 .

[18]  Yong Zhang,et al.  Sparse Approximation via Penalty Decomposition Methods , 2012, SIAM J. Optim..

[19]  Yonina C. Eldar,et al.  Sparsity Constrained Nonlinear Optimization: Optimality Conditions and Algorithms , 2012, SIAM J. Optim..

[20]  Jieping Ye,et al.  Large-scale sparse logistic regression , 2009, KDD.

[21]  Paul Tseng,et al.  Exact Regularization of Convex Programs , 2007, SIAM J. Optim..

[22]  Duan Li,et al.  OPTIMAL LOT SOLUTION TO CARDINALITY CONSTRAINED MEAN–VARIANCE FORMULATION FOR PORTFOLIO SELECTION , 2006 .

[23]  Jianli Chen,et al.  Lagrange Dual Method for Sparsity Constrained Optimization , 2018, IEEE Access.

[24]  Shabbir Ahmed,et al.  Exact augmented Lagrangian duality for mixed integer linear programming , 2017, Math. Program..

[25]  Benjamin Pfaff,et al.  Perturbation Analysis Of Optimization Problems , 2016 .

[26]  G. Kutyniok,et al.  Compressed Sensing , 2014 .

[27]  Jian Li,et al.  Linear Systems, Sparse Solutions, and Sudoku , 2010, IEEE Signal Processing Letters.

[28]  D. Donoho,et al.  Sparse nonnegative solution of underdetermined linear equations by linear programming. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[29]  R. Tyrrell Rockafellar,et al.  Variational Analysis , 1998, Grundlehren der mathematischen Wissenschaften.

[30]  W. Diewert.  Applications of Duality Theory , 1974 .