A proximal difference-of-convex algorithm with extrapolation
We consider a class of difference-of-convex (DC) optimization problems whose objective is level-bounded and is the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous concave function. While this kind of problems can be solved by the classical di...
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| Vydané v: | Computational optimization and applications Ročník 69; číslo 2; s. 297 - 324 |
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| Jazyk: | English |
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01.03.2018
Springer Nature B.V |
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| ISSN: | 0926-6003, 1573-2894 |
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| Abstract | We consider a class of difference-of-convex (DC) optimization problems whose objective is level-bounded and is the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous concave function. While this kind of problems can be solved by the classical difference-of-convex algorithm (DCA) (Pham et al. Acta Math Vietnam 22:289–355,
1997
), the difficulty of the subproblems of this algorithm depends heavily on the choice of DC decomposition. Simpler subproblems can be obtained by using a specific DC decomposition described in Pham et al. (SIAM J Optim 8:476–505,
1998
). This decomposition has been proposed in numerous work such as Gotoh et al. (DC formulations and algorithms for sparse optimization problems,
2017
), and we refer to the resulting DCA as the proximal DCA. Although the subproblems are simpler, the proximal DCA is the same as the proximal gradient algorithm when the concave part of the objective is void, and hence is potentially slow in practice. In this paper, motivated by the extrapolation techniques for accelerating the proximal gradient algorithm in the convex settings, we consider a proximal difference-of-convex algorithm with extrapolation to possibly accelerate the proximal DCA. We show that any cluster point of the sequence generated by our algorithm is a stationary point of the DC optimization problem for a fairly general choice of extrapolation parameters: in particular, the parameters can be chosen as in FISTA with fixed restart (O’Donoghue and Candès in Found Comput Math 15, 715–732,
2015
). In addition, by assuming the Kurdyka-Łojasiewicz property of the objective and the differentiability of the concave part, we establish global convergence of the sequence generated by our algorithm and analyze its convergence rate. Our numerical experiments on two difference-of-convex regularized least squares models show that our algorithm usually outperforms the proximal DCA and the general iterative shrinkage and thresholding algorithm proposed in Gong et al. (A general iterative shrinkage and thresholding algorithm for non-convex regularized optimization problems,
2013
). |
|---|---|
| AbstractList | We consider a class of difference-of-convex (DC) optimization problems whose objective is level-bounded and is the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous concave function. While this kind of problems can be solved by the classical difference-of-convex algorithm (DCA) (Pham et al. Acta Math Vietnam 22:289–355,
1997
), the difficulty of the subproblems of this algorithm depends heavily on the choice of DC decomposition. Simpler subproblems can be obtained by using a specific DC decomposition described in Pham et al. (SIAM J Optim 8:476–505,
1998
). This decomposition has been proposed in numerous work such as Gotoh et al. (DC formulations and algorithms for sparse optimization problems,
2017
), and we refer to the resulting DCA as the proximal DCA. Although the subproblems are simpler, the proximal DCA is the same as the proximal gradient algorithm when the concave part of the objective is void, and hence is potentially slow in practice. In this paper, motivated by the extrapolation techniques for accelerating the proximal gradient algorithm in the convex settings, we consider a proximal difference-of-convex algorithm with extrapolation to possibly accelerate the proximal DCA. We show that any cluster point of the sequence generated by our algorithm is a stationary point of the DC optimization problem for a fairly general choice of extrapolation parameters: in particular, the parameters can be chosen as in FISTA with fixed restart (O’Donoghue and Candès in Found Comput Math 15, 715–732,
2015
). In addition, by assuming the Kurdyka-Łojasiewicz property of the objective and the differentiability of the concave part, we establish global convergence of the sequence generated by our algorithm and analyze its convergence rate. Our numerical experiments on two difference-of-convex regularized least squares models show that our algorithm usually outperforms the proximal DCA and the general iterative shrinkage and thresholding algorithm proposed in Gong et al. (A general iterative shrinkage and thresholding algorithm for non-convex regularized optimization problems,
2013
). We consider a class of difference-of-convex (DC) optimization problems whose objective is level-bounded and is the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous concave function. While this kind of problems can be solved by the classical difference-of-convex algorithm (DCA) (Pham et al. Acta Math Vietnam 22:289–355, 1997), the difficulty of the subproblems of this algorithm depends heavily on the choice of DC decomposition. Simpler subproblems can be obtained by using a specific DC decomposition described in Pham et al. (SIAM J Optim 8:476–505, 1998). This decomposition has been proposed in numerous work such as Gotoh et al. (DC formulations and algorithms for sparse optimization problems, 2017), and we refer to the resulting DCA as the proximal DCA. Although the subproblems are simpler, the proximal DCA is the same as the proximal gradient algorithm when the concave part of the objective is void, and hence is potentially slow in practice. In this paper, motivated by the extrapolation techniques for accelerating the proximal gradient algorithm in the convex settings, we consider a proximal difference-of-convex algorithm with extrapolation to possibly accelerate the proximal DCA. We show that any cluster point of the sequence generated by our algorithm is a stationary point of the DC optimization problem for a fairly general choice of extrapolation parameters: in particular, the parameters can be chosen as in FISTA with fixed restart (O’Donoghue and Candès in Found Comput Math 15, 715–732, 2015). In addition, by assuming the Kurdyka-Łojasiewicz property of the objective and the differentiability of the concave part, we establish global convergence of the sequence generated by our algorithm and analyze its convergence rate. Our numerical experiments on two difference-of-convex regularized least squares models show that our algorithm usually outperforms the proximal DCA and the general iterative shrinkage and thresholding algorithm proposed in Gong et al. (A general iterative shrinkage and thresholding algorithm for non-convex regularized optimization problems, 2013). |
| Author | Chen, Xiaojun Wen, Bo Pong, Ting Kei |
| Author_xml | – sequence: 1 givenname: Bo surname: Wen fullname: Wen, Bo organization: School of Science, Hebei University of Technology, Department of Mathematics, Harbin Institute of Technology, Department of Applied Mathematics, The Hong Kong Polytechnic University – sequence: 2 givenname: Xiaojun orcidid: 0000-0001-8053-0121 surname: Chen fullname: Chen, Xiaojun email: maxjchen@polyu.edu.hk organization: Department of Applied Mathematics, The Hong Kong Polytechnic University – sequence: 3 givenname: Ting Kei surname: Pong fullname: Pong, Ting Kei organization: Department of Applied Mathematics, The Hong Kong Polytechnic University |
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| Cites_doi | 10.1007/978-1-4419-9569-8_10 10.1007/s10107-017-1181-0 10.1109/TSP.2014.2315167 10.1007/s10107-011-0484-9 10.1137/080716542 10.1007/978-1-4419-8853-9 10.1007/s10479-004-5022-1 10.1287/moor.1100.0449 10.1007/s10107-013-0701-9 10.1198/016214501753382273 10.1007/s10107-006-0034-z 10.1007/s10898-011-9765-3 10.1137/16M1084754 10.1007/s12532-011-0029-5 10.1007/s10107-007-0133-5 10.1109/TSP.2009.2016892 10.1007/s00041-008-9045-x 10.1137/050644641 10.1214/09-AOS729 10.1007/s10589-017-9900-2 10.1007/s10208-013-9150-3 10.1109/TSP.2014.2303946 10.1137/15M1028054 10.1007/s10107-012-0629-5 10.1016/0041-5553(64)90137-5 10.1007/978-3-642-02431-3 10.1137/S1052623494274313 10.1137/140952363 10.1007/978-3-319-31484-6 10.1287/moor.2016.0837 10.1007/s10208-017-9366-8 |
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| References | ZhangCNearly unbiased variable selection under minimax concave penaltyAnn. Stat.201038894942260470110.1214/09-AOS7291183.62120 AlvaradoAScutariGPangJSA new decomposition method for multiuser DC-programming and its applicationsIEEE Trans. Signal Process.20146229842998322516010.1109/TSP.2014.2315167 NesterovYGradient methods for minimizing composite functionsMath. Progr. Ser. B2013140125161307186510.1007/s10107-012-0629-51287.90067 PolyakBTSome methods of speeding up the convergence of iteration methodsUSSR Comput. Math. Math. Phys.1964411710.1016/0041-5553(64)90137-5 YinPLouYHeQXinJMinimization of ℓ1-2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{1-2}$$\end{document} for compressed sensingSIAM J. Sci. Comput.201537A536A563331522910.1137/1409523631316.90037 AttouchHBolteJSvaiterBFConvergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss-Seidel methodsMath. Progr. Ser. A201313791129301042110.1007/s10107-011-0484-91260.49048 NesterovYDual extrapolation and its applications to solving variational inequalities and related problemsMath. Progr. Ser. B2007109319344229514610.1007/s10107-006-0034-z1167.90014 AttouchHBolteJRedontPSoubeyranAProximal alternating minimization and projection methods for nonconvex problems: an approach based on the Kurdyka-Łojasiewicz inequalityMath. Oper. Res.201035438457267472810.1287/moor.1100.04491214.65036 Le ThiHAPhamDTLeDMExact penalty in D.C. programmingVietnam J. Math.19992716917818108951006.90062 Bian, W., Chen, X.: Optimality and complexity for constrained optimization problems with nonconvex regularization. Math. Oper. Res. (2017). doi:10.1287/moor.2016.0837 CombettesPLPesquetJ-CProximal splitting methods in signal processingFixed-Point Algorithms Inverse Probl. Sci. Eng.201149185212285883810.1007/978-1-4419-9569-8_101242.90160 NesterovYA method of solving a convex programming problem with convergence rate O(1k2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\frac{1}{k^2})$$\end{document}Sov. Math. Dokl.1983273723760535.90071 FanJLiRVariable selection via nonconcave penalized likelihood and its oracle propertiesJ. Am. Stat. Assoc.20019613481360194658110.1198/0162145017533822731073.62547 PhamDTLe ThiHAA D.C. optimization algorithm for solving the trust-region subproblemSIAM J. Optim.19988476505161853110.1137/S10526234942743130913.65054 SanjabiMRazaviyaynMLuoZ-QOptimal joint base station assignment and beamforming for heterogeneous networksIEEE Trans. Signal Process.20146219501961319519010.1109/TSP.2014.2303946 LiuTPongTKFurther properties of the forward-backward envelope with applications to difference-of-convex programmingComput. Optim. Appl.201767489520365418310.1007/s10589-017-9900-206748147 WrightSJNowakRFigueiredoMATSparse reconstruction by separable approximationIEEE Trans. Signal Process.20095724792493265016510.1109/TSP.2009.2016892 Gong, P., Zhang, C., Lu, Z., Huang, J., Ye, J.: A general iterative shrinkage and thresholding algorithm for non-convex regularized optimization problems. In: ICML (2013) ChenXLuZPongTKPenalty methods for a class of non-Lipschitz optimization problemsSIAM J. Optim.20162614651492352308510.1137/15M10280541342.90181 NesterovYIntroductory Lectures on Convex Optimization: A Basic Course2004BostonKluwer Academic Publishers10.1007/978-1-4419-8853-91086.90045 BeckATeboulleMA fast iterative shrinkage-thresholding algorithm for linear inverse problemsSIAM J. Imaging Sci.20092183202248652710.1137/0807165421175.94009 Zhang, S., Xin, J.: Minimization of transformed L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_1$$\end{document} penalty: theory, difference of convex function algorithm, and robust application in compressed sensing. arXiv preprint arXiv:1411.5735v3 Li, G., Pong, T.K.: Calculus of the exponent of Kurdyka-Łojasiewicz inequality and its applications to linear convergence of first-order methods. Found. Comput. Math. (2017). doi:10.1007/s10208-017-9366-8 Le ThiHAPhamDTHuynhVNExact penalty and error bounds in DC programmingJ. Glob. Optim.201252509535289253410.1007/s10898-011-9765-31242.49037 BeckerSCandèsEJGrantMCTemplates for convex cone problems with applications to sparse signal recoveryMath. Progr. Comput.20113165218283326210.1007/s12532-011-0029-51257.90042 BolteJSabachSTeboulleMProximal alternating linearized minimization for nonconvex and nonsmooth problemsMath. Progr. Ser. A2014146459494323262310.1007/s10107-013-0701-91297.90125 RockafellarRTWetsRJ-BVariational Analysis1998BerlinSpringer10.1007/978-3-642-02431-30888.49001 Le ThiHAPhamDTThe DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problemsAnn. Oper. Res.20051332346211931110.1007/s10479-004-5022-11116.90122 Banert, S., Boţ, R.I.: A general double-proximal gradient algorithm for d.c. programming. arXiv preprint arXiv:1610.06538v1 Gotoh, J., Takeda, A., Tono, K.: DC formulations and algorithms for sparse optimization problems. Math. Progr. Ser. B. (2017). doi:10.1007/s10107-017-1181-0 Ahn, M., Pang, J.S., Xin, J.: Difference-of-convex learning: directional stationarity, optimality, and sparsity. SIAM J. Optim. 27, 1637–1665 (2017) TuyHConvex Analysis and Global Optimization20162BerlinSpringer10.1007/978-3-319-31484-61362.90001 AttouchHBolteJOn the convergence of the proximal algorithm for nonsmooth functions involving analytic featuresMath. Progr. Ser. B2009116516242127010.1007/s10107-007-0133-51165.90018 CandèsEJWakinMBoydSEnhancing sparsity by reweighted ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{1}$$\end{document} minimizationJ. Fourier Anal. Appl.200814877905246161110.1007/s00041-008-9045-x1176.94014 BolteJDaniilidisALewisAThe Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systemsSIAM J. Optim.2007171205122310.1137/0506446411129.26012 PhamDTLe ThiHAConvex analysis approach to D.C. programming: theory, algorithms and applicationsActa Math. Vietnam.19972228935514797510895.90152 O’DonoghueBCandèsEJAdaptive restart for accelerated gradient schemesFound. Comput. 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| References_xml | – reference: PhamDTLe ThiHAConvex analysis approach to D.C. programming: theory, algorithms and applicationsActa Math. Vietnam.19972228935514797510895.90152 – reference: PhamDTLe ThiHAA D.C. optimization algorithm for solving the trust-region subproblemSIAM J. Optim.19988476505161853110.1137/S10526234942743130913.65054 – reference: WrightSJNowakRFigueiredoMATSparse reconstruction by separable approximationIEEE Trans. Signal Process.20095724792493265016510.1109/TSP.2009.2016892 – reference: AttouchHBolteJSvaiterBFConvergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss-Seidel methodsMath. Progr. Ser. A201313791129301042110.1007/s10107-011-0484-91260.49048 – reference: BeckATeboulleMA fast iterative shrinkage-thresholding algorithm for linear inverse problemsSIAM J. Imaging Sci.20092183202248652710.1137/0807165421175.94009 – reference: BolteJSabachSTeboulleMProximal alternating linearized minimization for nonconvex and nonsmooth problemsMath. Progr. Ser. A2014146459494323262310.1007/s10107-013-0701-91297.90125 – reference: CombettesPLPesquetJ-CProximal splitting methods in signal processingFixed-Point Algorithms Inverse Probl. Sci. Eng.201149185212285883810.1007/978-1-4419-9569-8_101242.90160 – reference: Le ThiHAPhamDTLeDMExact penalty in D.C. programmingVietnam J. Math.19992716917818108951006.90062 – reference: RockafellarRTWetsRJ-BVariational Analysis1998BerlinSpringer10.1007/978-3-642-02431-30888.49001 – reference: YinPLouYHeQXinJMinimization of ℓ1-2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{1-2}$$\end{document} for compressed sensingSIAM J. Sci. Comput.201537A536A563331522910.1137/1409523631316.90037 – reference: Ahn, M., Pang, J.S., Xin, J.: Difference-of-convex learning: directional stationarity, optimality, and sparsity. SIAM J. Optim. 27, 1637–1665 (2017) – reference: BolteJDaniilidisALewisAThe Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systemsSIAM J. Optim.2007171205122310.1137/0506446411129.26012 – reference: Gotoh, J., Takeda, A., Tono, K.: DC formulations and algorithms for sparse optimization problems. Math. Progr. Ser. B. (2017). doi:10.1007/s10107-017-1181-0 – reference: Banert, S., Boţ, R.I.: A general double-proximal gradient algorithm for d.c. programming. arXiv preprint arXiv:1610.06538v1 – reference: NesterovYIntroductory Lectures on Convex Optimization: A Basic Course2004BostonKluwer Academic Publishers10.1007/978-1-4419-8853-91086.90045 – reference: NesterovYGradient methods for minimizing composite functionsMath. Progr. Ser. B2013140125161307186510.1007/s10107-012-0629-51287.90067 – reference: PolyakBTSome methods of speeding up the convergence of iteration methodsUSSR Comput. Math. Math. Phys.1964411710.1016/0041-5553(64)90137-5 – reference: AttouchHBolteJRedontPSoubeyranAProximal alternating minimization and projection methods for nonconvex problems: an approach based on the Kurdyka-Łojasiewicz inequalityMath. Oper. Res.201035438457267472810.1287/moor.1100.04491214.65036 – reference: AttouchHBolteJOn the convergence of the proximal algorithm for nonsmooth functions involving analytic featuresMath. Progr. Ser. B2009116516242127010.1007/s10107-007-0133-51165.90018 – reference: CandèsEJWakinMBoydSEnhancing sparsity by reweighted ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{1}$$\end{document} minimizationJ. Fourier Anal. Appl.200814877905246161110.1007/s00041-008-9045-x1176.94014 – reference: LiuTPongTKFurther properties of the forward-backward envelope with applications to difference-of-convex programmingComput. Optim. Appl.201767489520365418310.1007/s10589-017-9900-206748147 – reference: ChenXLuZPongTKPenalty methods for a class of non-Lipschitz optimization problemsSIAM J. Optim.20162614651492352308510.1137/15M10280541342.90181 – reference: TuyHConvex Analysis and Global Optimization20162BerlinSpringer10.1007/978-3-319-31484-61362.90001 – reference: Gong, P., Zhang, C., Lu, Z., Huang, J., Ye, J.: A general iterative shrinkage and thresholding algorithm for non-convex regularized optimization problems. In: ICML (2013) – reference: Li, G., Pong, T.K.: Calculus of the exponent of Kurdyka-Łojasiewicz inequality and its applications to linear convergence of first-order methods. Found. Comput. Math. (2017). doi:10.1007/s10208-017-9366-8 – reference: BeckerSCandèsEJGrantMCTemplates for convex cone problems with applications to sparse signal recoveryMath. Progr. Comput.20113165218283326210.1007/s12532-011-0029-51257.90042 – reference: Le ThiHAPhamDTThe DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problemsAnn. Oper. Res.20051332346211931110.1007/s10479-004-5022-11116.90122 – reference: SanjabiMRazaviyaynMLuoZ-QOptimal joint base station assignment and beamforming for heterogeneous networksIEEE Trans. Signal Process.20146219501961319519010.1109/TSP.2014.2303946 – reference: NesterovYDual extrapolation and its applications to solving variational inequalities and related problemsMath. Progr. Ser. B2007109319344229514610.1007/s10107-006-0034-z1167.90014 – reference: Zhang, S., Xin, J.: Minimization of transformed L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_1$$\end{document} penalty: theory, difference of convex function algorithm, and robust application in compressed sensing. arXiv preprint arXiv:1411.5735v3 – reference: AlvaradoAScutariGPangJSA new decomposition method for multiuser DC-programming and its applicationsIEEE Trans. Signal Process.20146229842998322516010.1109/TSP.2014.2315167 – reference: NesterovYA method of solving a convex programming problem with convergence rate O(1k2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\frac{1}{k^2})$$\end{document}Sov. Math. Dokl.1983273723760535.90071 – reference: O’DonoghueBCandèsEJAdaptive restart for accelerated gradient schemesFound. Comput. Math.201515715732334817110.1007/s10208-013-9150-31320.90061 – reference: FanJLiRVariable selection via nonconcave penalized likelihood and its oracle propertiesJ. Am. Stat. Assoc.20019613481360194658110.1198/0162145017533822731073.62547 – reference: Bian, W., Chen, X.: Optimality and complexity for constrained optimization problems with nonconvex regularization. Math. Oper. Res. (2017). doi:10.1287/moor.2016.0837 – reference: Le ThiHAPhamDTHuynhVNExact penalty and error bounds in DC programmingJ. Glob. Optim.201252509535289253410.1007/s10898-011-9765-31242.49037 – reference: ZhangCNearly unbiased variable selection under minimax concave penaltyAnn. Stat.201038894942260470110.1214/09-AOS7291183.62120 – volume: 49 start-page: 185 year: 2011 ident: 9954_CR14 publication-title: Fixed-Point Algorithms Inverse Probl. Sci. Eng. doi: 10.1007/978-1-4419-9569-8_10 – ident: 9954_CR17 doi: 10.1007/s10107-017-1181-0 – ident: 9954_CR16 – ident: 9954_CR37 – volume: 62 start-page: 2984 year: 2014 ident: 9954_CR2 publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2014.2315167 – volume: 137 start-page: 91 year: 2013 ident: 9954_CR5 publication-title: Math. Progr. Ser. A doi: 10.1007/s10107-011-0484-9 – volume: 27 start-page: 169 year: 1999 ident: 9954_CR19 publication-title: Vietnam J. Math. – volume: 2 start-page: 183 year: 2009 ident: 9954_CR7 publication-title: SIAM J. Imaging Sci. doi: 10.1137/080716542 – volume-title: Introductory Lectures on Convex Optimization: A Basic Course year: 2004 ident: 9954_CR24 doi: 10.1007/978-1-4419-8853-9 – volume: 133 start-page: 23 year: 2005 ident: 9954_CR18 publication-title: Ann. Oper. Res. doi: 10.1007/s10479-004-5022-1 – volume: 35 start-page: 438 year: 2010 ident: 9954_CR4 publication-title: Math. Oper. Res. doi: 10.1287/moor.1100.0449 – volume: 146 start-page: 459 year: 2014 ident: 9954_CR11 publication-title: Math. Progr. Ser. A doi: 10.1007/s10107-013-0701-9 – volume: 96 start-page: 1348 year: 2001 ident: 9954_CR15 publication-title: J. Am. Stat. Assoc. doi: 10.1198/016214501753382273 – volume: 109 start-page: 319 year: 2007 ident: 9954_CR25 publication-title: Math. Progr. Ser. B doi: 10.1007/s10107-006-0034-z – volume: 52 start-page: 509 year: 2012 ident: 9954_CR20 publication-title: J. Glob. Optim. doi: 10.1007/s10898-011-9765-3 – ident: 9954_CR1 doi: 10.1137/16M1084754 – volume: 3 start-page: 165 year: 2011 ident: 9954_CR8 publication-title: Math. Progr. Comput. doi: 10.1007/s12532-011-0029-5 – volume: 116 start-page: 5 year: 2009 ident: 9954_CR3 publication-title: Math. Progr. Ser. B doi: 10.1007/s10107-007-0133-5 – volume: 57 start-page: 2479 year: 2009 ident: 9954_CR34 publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2009.2016892 – volume: 14 start-page: 877 year: 2008 ident: 9954_CR12 publication-title: J. Fourier Anal. Appl. doi: 10.1007/s00041-008-9045-x – volume: 17 start-page: 1205 year: 2007 ident: 9954_CR10 publication-title: SIAM J. Optim. doi: 10.1137/050644641 – volume: 38 start-page: 894 year: 2010 ident: 9954_CR36 publication-title: Ann. Stat. doi: 10.1214/09-AOS729 – volume: 67 start-page: 489 year: 2017 ident: 9954_CR22 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-017-9900-2 – volume: 15 start-page: 715 year: 2015 ident: 9954_CR27 publication-title: Found. Comput. Math. doi: 10.1007/s10208-013-9150-3 – volume: 62 start-page: 1950 year: 2014 ident: 9954_CR32 publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2014.2303946 – volume: 26 start-page: 1465 year: 2016 ident: 9954_CR13 publication-title: SIAM J. Optim. doi: 10.1137/15M1028054 – volume: 27 start-page: 372 year: 1983 ident: 9954_CR23 publication-title: Sov. Math. Dokl. – volume: 140 start-page: 125 year: 2013 ident: 9954_CR26 publication-title: Math. Progr. Ser. B doi: 10.1007/s10107-012-0629-5 – volume: 22 start-page: 289 year: 1997 ident: 9954_CR28 publication-title: Acta Math. Vietnam. – volume: 4 start-page: 1 year: 1964 ident: 9954_CR30 publication-title: USSR Comput. Math. Math. Phys. doi: 10.1016/0041-5553(64)90137-5 – volume-title: Variational Analysis year: 1998 ident: 9954_CR31 doi: 10.1007/978-3-642-02431-3 – volume: 8 start-page: 476 year: 1998 ident: 9954_CR29 publication-title: SIAM J. Optim. doi: 10.1137/S1052623494274313 – volume: 37 start-page: A536 year: 2015 ident: 9954_CR35 publication-title: SIAM J. Sci. Comput. doi: 10.1137/140952363 – volume-title: Convex Analysis and Global Optimization year: 2016 ident: 9954_CR33 doi: 10.1007/978-3-319-31484-6 – ident: 9954_CR9 doi: 10.1287/moor.2016.0837 – ident: 9954_CR21 doi: 10.1007/s10208-017-9366-8 – ident: 9954_CR6 |
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