A fast dual proximal gradient algorithm for convex minimization and applications
We consider the convex composite problem of minimizing the sum of a strongly convex function and a general extended valued convex function. We present a dual-based proximal gradient scheme for solving this problem. We show that although the rate of convergence of the dual objective function sequence...
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| Veröffentlicht in: | Operations research letters Jg. 42; H. 1; S. 1 - 6 |
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01.01.2014
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| Abstract | We consider the convex composite problem of minimizing the sum of a strongly convex function and a general extended valued convex function. We present a dual-based proximal gradient scheme for solving this problem. We show that although the rate of convergence of the dual objective function sequence converges to the optimal value with the rate O(1/k2), the rate of convergence of the primal sequence is of the order O(1/k). |
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| AbstractList | We consider the convex composite problem of minimizing the sum of a strongly convex function and a general extended valued convex function. We present a dual-based proximal gradient scheme for solving this problem. We show that although the rate of convergence of the dual objective function sequence converges to the optimal value with the rate O(1/k2), the rate of convergence of the primal sequence is of the order O(1/k). We consider the convex composite problem of minimizing the sum of a strongly convex function and a general extended valued convex function. We present a dual-based proximal gradient scheme for solving this problem. We show that although the rate of convergence of the dual objective function sequence converges to the optimal value with the rate O(1/k super(2))O(1/k2), the rate of convergence of the primal sequence is of the order O(1/k)O(1/k). |
| Author | Teboulle, Marc Beck, Amir |
| Author_xml | – sequence: 1 givenname: Amir surname: Beck fullname: Beck, Amir email: becka@ie.technion.ac.il organization: Faculty of Industrial Engineering and Management, Technion - Israel Institute of Technology, Haifa, Israel – sequence: 2 givenname: Marc surname: Teboulle fullname: Teboulle, Marc email: teboulle@post.tau.ac.il organization: School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Israel |
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| Cites_doi | 10.1137/0314056 10.1137/070696143 10.1109/TIP.2009.2028250 10.24033/bsmf.1625 10.1109/TIP.2010.2072512 10.1016/S0167-6377(02)00231-6 10.1137/080716542 10.1007/s11228-010-0147-7 10.1007/s10107-007-0147-z 10.1137/0329006 10.1016/0022-247X(79)90234-8 10.1561/2200000016 |
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| References | Boyd, Parikh, Chu, Peleato, Eckstein (br000030) 2011; 3 Glowinski, Le Tallec (br000060) 1989 Gabay (br000055) 1983 Chambolle (br000035) 2004; 20 Beck, Teboulle (br000015) 2009; 18 Beck, Teboulle (br000020) 2009; 2 Nemirovsky, Yudin (br000070) 1983 Uzawa (br000105) 1958 Rockafellar (br000085) 1970 Y. Nesterov, Gradient methods for minimizing composite objective function. 2007. CORE Report. Available at . Beck, Teboulle (br000010) 2003; 31 Combettes, Dũng, Vũ (br000040) 2010; 18 Moreau (br000065) 1965; 93 Passty (br000080) 1979; 72 Weiss, Blanc-Féraud, Aubert (br000110) 2009; 31 Auslender, Teboulle (br000005) 2009; 120 Rockafellar (br000090) 1976; 14 Rockafellar, Wets (br000095) 1998; vol. 317 Tseng (br000100) 1991; 29 Fadili, Peyré (br000050) 2011; 20 Bertsekas (br000025) 1982 Combettes, Presquet (br000045) 2011 10.1016/j.orl.2013.10.007_br000075 Glowinski (10.1016/j.orl.2013.10.007_br000060) 1989 Nemirovsky (10.1016/j.orl.2013.10.007_br000070) 1983 Tseng (10.1016/j.orl.2013.10.007_br000100) 1991; 29 Weiss (10.1016/j.orl.2013.10.007_br000110) 2009; 31 Combettes (10.1016/j.orl.2013.10.007_br000045) 2011 Combettes (10.1016/j.orl.2013.10.007_br000040) 2010; 18 Passty (10.1016/j.orl.2013.10.007_br000080) 1979; 72 Beck (10.1016/j.orl.2013.10.007_br000020) 2009; 2 Rockafellar (10.1016/j.orl.2013.10.007_br000095) 1998; vol. 317 Beck (10.1016/j.orl.2013.10.007_br000010) 2003; 31 Fadili (10.1016/j.orl.2013.10.007_br000050) 2011; 20 Uzawa (10.1016/j.orl.2013.10.007_br000105) 1958 Boyd (10.1016/j.orl.2013.10.007_br000030) 2011; 3 Rockafellar (10.1016/j.orl.2013.10.007_br000085) 1970 Beck (10.1016/j.orl.2013.10.007_br000015) 2009; 18 Chambolle (10.1016/j.orl.2013.10.007_br000035) 2004; 20 Moreau (10.1016/j.orl.2013.10.007_br000065) 1965; 93 Rockafellar (10.1016/j.orl.2013.10.007_br000090) 1976; 14 Gabay (10.1016/j.orl.2013.10.007_br000055) 1983 Auslender (10.1016/j.orl.2013.10.007_br000005) 2009; 120 Bertsekas (10.1016/j.orl.2013.10.007_br000025) 1982 |
| References_xml | – start-page: 185 year: 2011 end-page: 212 ident: br000045 article-title: Proximal splitting methods in signal processing publication-title: Fixed-Point Algorithms for Inverse Problems in Science and Engineering – volume: vol. 317 year: 1998 ident: br000095 publication-title: Variational Analysis – volume: 31 start-page: 2047 year: 2009 end-page: 2080 ident: br000110 article-title: Efficient schemes for total variation minimization under constraints in image processing publication-title: SIAM J. Sci. Comput. – volume: 120 start-page: 37 year: 2009 end-page: 48 ident: br000005 article-title: Projected subgradient methods with non-Euclidean distances for non-differentiable convex minimization and variational inequalities publication-title: Math. Program. – volume: 2 start-page: 183 year: 2009 end-page: 202 ident: br000020 article-title: A fast iterative shrinkage-thresholding algorithm for linear inverse problems publication-title: SIAM J. Imaging Sci. – volume: 14 start-page: 877 year: 1976 end-page: 898 ident: br000090 article-title: Monotone operators and the proximal point algorithm publication-title: SIAM J. Control Optim. – volume: 3 start-page: 1 year: 2011 end-page: 122 ident: br000030 article-title: Distributed optimization and statistical learning via the alternating direction method of multipliers publication-title: Found. Trends Mach. Learn. – volume: 72 start-page: 383 year: 1979 end-page: 390 ident: br000080 article-title: Ergodic convergence to a zero of the sum of monotone operators in Hilbert space publication-title: J. Math. Anal. Appl. – reference: Y. Nesterov, Gradient methods for minimizing composite objective function. 2007. CORE Report. Available at – start-page: 299 year: 1983 end-page: 340 ident: br000055 article-title: Applications of the method of multipliers to variational inequalities publication-title: Augmented Lagrangian Methods: Applications to the Solution of Boundary Value Problems, Chapter IX – reference: . – year: 1970 ident: br000085 article-title: Convex Analysis – volume: 29 start-page: 119 year: 1991 end-page: 138 ident: br000100 article-title: Applications of a splitting algorithm to decomposition in convex programming and variational inequalities publication-title: SIAM J. Control Optim. – start-page: 154 year: 1958 end-page: 165 ident: br000105 article-title: Iterative methods for concave programming publication-title: Studies in Linear and Nonlinear Programming – year: 1983 ident: br000070 article-title: Problem complexity and method efficiency in optimization publication-title: A Wiley-Interscience Publication – year: 1982 ident: br000025 article-title: Constrained Optimization and Lagrangian Multipliers – volume: 31 start-page: 167 year: 2003 end-page: 175 ident: br000010 article-title: Mirror descent and nonlinear projected subgradient methods for convex optimization publication-title: Oper. Res. Lett. – volume: 20 start-page: 89 year: 2004 end-page: 97 ident: br000035 article-title: An algorithm for total variation minimization and applications publication-title: J. Math. Imaging Vision – volume: 18 start-page: 2419 year: 2009 end-page: 2434 ident: br000015 article-title: Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems publication-title: IEEE Trans. Image Process. – volume: 93 start-page: 273 year: 1965 end-page: 299 ident: br000065 article-title: Proximité et dualité dans un espace hilbertien publication-title: Bull. Soc. Math. France – volume: 18 start-page: 373 year: 2010 end-page: 404 ident: br000040 article-title: Dualization of signal recovery problems publication-title: Set-Valued Var. Anal. – volume: 20 start-page: 657 year: 2011 end-page: 669 ident: br000050 article-title: Total variation projection with first order schemes publication-title: IEEE Trans. Image Process. – year: 1989 ident: br000060 publication-title: Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics, volume 9 – ident: 10.1016/j.orl.2013.10.007_br000075 – volume: 14 start-page: 877 issue: 5 year: 1976 ident: 10.1016/j.orl.2013.10.007_br000090 article-title: Monotone operators and the proximal point algorithm publication-title: SIAM J. Control Optim. doi: 10.1137/0314056 – volume: 31 start-page: 2047 year: 2009 ident: 10.1016/j.orl.2013.10.007_br000110 article-title: Efficient schemes for total variation minimization under constraints in image processing publication-title: SIAM J. Sci. Comput. doi: 10.1137/070696143 – volume: vol. 317 year: 1998 ident: 10.1016/j.orl.2013.10.007_br000095 – volume: 18 start-page: 2419 year: 2009 ident: 10.1016/j.orl.2013.10.007_br000015 article-title: Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2009.2028250 – year: 1989 ident: 10.1016/j.orl.2013.10.007_br000060 – volume: 93 start-page: 273 year: 1965 ident: 10.1016/j.orl.2013.10.007_br000065 article-title: Proximité et dualité dans un espace hilbertien publication-title: Bull. Soc. Math. France doi: 10.24033/bsmf.1625 – volume: 20 start-page: 89 issue: 1–2 year: 2004 ident: 10.1016/j.orl.2013.10.007_br000035 article-title: An algorithm for total variation minimization and applications publication-title: J. Math. Imaging Vision – volume: 20 start-page: 657 year: 2011 ident: 10.1016/j.orl.2013.10.007_br000050 article-title: Total variation projection with first order schemes publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2010.2072512 – volume: 31 start-page: 167 year: 2003 ident: 10.1016/j.orl.2013.10.007_br000010 article-title: Mirror descent and nonlinear projected subgradient methods for convex optimization publication-title: Oper. Res. Lett. doi: 10.1016/S0167-6377(02)00231-6 – volume: 2 start-page: 183 issue: 1 year: 2009 ident: 10.1016/j.orl.2013.10.007_br000020 article-title: A fast iterative shrinkage-thresholding algorithm for linear inverse problems publication-title: SIAM J. Imaging Sci. doi: 10.1137/080716542 – volume: 18 start-page: 373 issue: 3–4 year: 2010 ident: 10.1016/j.orl.2013.10.007_br000040 article-title: Dualization of signal recovery problems publication-title: Set-Valued Var. Anal. doi: 10.1007/s11228-010-0147-7 – year: 1983 ident: 10.1016/j.orl.2013.10.007_br000070 article-title: Problem complexity and method efficiency in optimization – year: 1970 ident: 10.1016/j.orl.2013.10.007_br000085 – volume: 120 start-page: 37 year: 2009 ident: 10.1016/j.orl.2013.10.007_br000005 article-title: Projected subgradient methods with non-Euclidean distances for non-differentiable convex minimization and variational inequalities publication-title: Math. Program. doi: 10.1007/s10107-007-0147-z – year: 1982 ident: 10.1016/j.orl.2013.10.007_br000025 – volume: 29 start-page: 119 issue: 1 year: 1991 ident: 10.1016/j.orl.2013.10.007_br000100 article-title: Applications of a splitting algorithm to decomposition in convex programming and variational inequalities publication-title: SIAM J. Control Optim. doi: 10.1137/0329006 – start-page: 299 year: 1983 ident: 10.1016/j.orl.2013.10.007_br000055 article-title: Applications of the method of multipliers to variational inequalities – start-page: 154 year: 1958 ident: 10.1016/j.orl.2013.10.007_br000105 article-title: Iterative methods for concave programming – start-page: 185 year: 2011 ident: 10.1016/j.orl.2013.10.007_br000045 article-title: Proximal splitting methods in signal processing – volume: 72 start-page: 383 issue: 2 year: 1979 ident: 10.1016/j.orl.2013.10.007_br000080 article-title: Ergodic convergence to a zero of the sum of monotone operators in Hilbert space publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(79)90234-8 – volume: 3 start-page: 1 issue: 1 year: 2011 ident: 10.1016/j.orl.2013.10.007_br000030 article-title: Distributed optimization and statistical learning via the alternating direction method of multipliers publication-title: Found. Trends Mach. Learn. doi: 10.1561/2200000016 |
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| Title | A fast dual proximal gradient algorithm for convex minimization and applications |
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