-
2
-
-
0032385816
-
On gradients of functions definable in o-minimal structures
-
Kurdyka, K.: On gradients of functions definable in o-minimal structures. Ann. Inst. Fourier 48, 769–783 (1998)
-
(1998)
Ann. Inst. Fourier
, vol.48
, pp. 769-783
-
-
Kurdyka, K.1
-
3
-
-
0001228050
-
Sur la géométrie semi- et sous-analytique
-
Łojasiewicz, S.: Sur la géométrie semi- et sous-analytique. Ann. Inst. Fourier 43, 1575–1595 (1993)
-
(1993)
Ann. Inst. Fourier
, vol.43
, pp. 1575-1595
-
-
Łojasiewicz, S.1
-
4
-
-
0013477144
-
(formula presented)-stratification of subanalytic functions and the Łojasiewicz inequality
-
Kurdyka, K., Parusiński, A.: $$\mathbf{w}_f$$wf-stratification of subanalytic functions and the Łojasiewicz inequality. C. R. Acad. Paris 318, 129–133 (1994)
-
(1994)
C. R. Acad. Paris
, vol.318
, pp. 129-133
-
-
Kurdyka, K.1
Parusiński, A.2
-
5
-
-
36249023228
-
The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems
-
Bolte, J., Daniilidis, A., Lewis, A.: The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems. SIAM J. Optim. 17, 1205–1223 (2006)
-
(2006)
SIAM J. Optim
, vol.17
, pp. 1205-1223
-
-
Bolte, J.1
Daniilidis, A.2
Lewis, A.3
-
6
-
-
0000137102
-
Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems
-
Simon, L.: Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems. Ann. Math. 118, 525–571 (1983)
-
(1983)
Ann. Math
, vol.118
, pp. 525-571
-
-
Simon, L.1
-
7
-
-
0013145570
-
Convergence in gradient-like systems which are asymptotically autonomous and analytic
-
Huang, S.-Z., Takáč, P.: Convergence in gradient-like systems which are asymptotically autonomous and analytic. Nonlinear Anal. Ser. A Theory Methods 46, 675–698 (2001)
-
(2001)
Nonlinear Anal. Ser. A Theory Methods
, vol.46
, pp. 675-698
-
-
Huang, S.-Z.1
Takáč, P.2
-
8
-
-
0037410017
-
Convergence to steady states in asymptotically autonomous semilinear evolution equations
-
Chill, R., Jendoubi, M.A.: Convergence to steady states in asymptotically autonomous semilinear evolution equations. Nonlinear Anal. 53, 1017–1039 (2003)
-
(2003)
Nonlinear Anal
, vol.53
, pp. 1017-1039
-
-
Chill, R.1
Jendoubi, M.A.2
-
9
-
-
0000746952
-
Convergence of solutions of second-order gradient-like systems with analytic nonlinearities
-
Haraux, A., Jendoubi, M.A.: Convergence of solutions of second-order gradient-like systems with analytic nonlinearities. J. Differ. Equ. 144(2), 313–320 (1998)
-
(1998)
J. Differ. Equ
, vol.144
, Issue.2
, pp. 313-320
-
-
Haraux, A.1
Jendoubi, M.A.2
-
11
-
-
41949123114
-
Constructive solution of a bilinear optimal control problem for a Schrödinger equation
-
Baudoin, L., Salomon, J.: Constructive solution of a bilinear optimal control problem for a Schrödinger equation. Syst. Control Lett. 57(6), 453–464 (2008)
-
(2008)
Syst. Control Lett
, vol.57
, Issue.6
, pp. 453-464
-
-
Baudoin, L.1
Salomon, J.2
-
12
-
-
33646735617
-
Convergence of the iterates of descent methods for analytic cost functions
-
Absil, P.-A., Mahony, R., Andrews, B.: Convergence of the iterates of descent methods for analytic cost functions. SIAM J. Optim. 16, 531–547 (2005)
-
(2005)
SIAM J. Optim
, vol.16
, pp. 531-547
-
-
Absil, P.-A.1
Mahony, R.2
Andrews, B.3
-
13
-
-
45749101721
-
On the convergence of the proximal algorithm for nonsmooth functions involving analytic features
-
Attouch, H., Bolte, J.: On the convergence of the proximal algorithm for nonsmooth functions involving analytic features. Math. Program. Ser. B 116, 5–16 (2009)
-
(2009)
Math. Program. Ser. B
, vol.116
, pp. 5-16
-
-
Attouch, H.1
Bolte, J.2
-
14
-
-
77951625247
-
Characterizations of Łojasiewicz inequalities: subgradient flows, talweg, convexity
-
Bolte, J., Daniilidis, A., Ley, O., Mazet, L.: Characterizations of Łojasiewicz inequalities: subgradient flows, talweg, convexity. Trans. Am. Math. Soc. 362, 3319–3363 (2010)
-
(2010)
Trans. Am. Math. Soc
, vol.362
, pp. 3319-3363
-
-
Bolte, J.1
Daniilidis, A.2
Ley, O.3
Mazet, L.4
-
15
-
-
77249098380
-
Convergence to equilibrium for the backward Euler scheme and applications
-
Merlet, B., Pierre, M.: Convergence to equilibrium for the backward Euler scheme and applications. Commun. Pure Appl. Anal 9, 685–702 (2010)
-
(2010)
Commun. Pure Appl. Anal
, vol.9
, pp. 685-702
-
-
Merlet, B.1
Pierre, M.2
-
16
-
-
84896488221
-
Convergence of non-smooth descent methods using the Kurdyka–Lojasiewicz inequality
-
Noll, D.: Convergence of non-smooth descent methods using the Kurdyka–Lojasiewicz inequality. J. Optim. Theory Appl. 160, 553–572 (2014)
-
(2014)
J. Optim. Theory Appl
, vol.160
, pp. 553-572
-
-
Noll, D.1
-
17
-
-
84877887498
-
Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss–Seidel methods
-
Attouch, H., Bolte, J., Svaiter, B.F.: Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss–Seidel methods. Math. Program. 137(1–2), 91–129 (2013)
-
(2013)
Math. Program
, vol.137
, Issue.1-2
, pp. 91-129
-
-
Attouch, H.1
Bolte, J.2
Svaiter, B.F.3
-
19
-
-
77953092582
-
Proximal alternating minimization and projection methods for nonconvex problems. An approach based on the Kurdyka–Łojasiewicz inequality
-
Attouch, H., Bolte, J., Redont, P., Soubeyran, A.: Proximal alternating minimization and projection methods for nonconvex problems. An approach based on the Kurdyka–Łojasiewicz inequality. Math. Oper. Res. 35(2), 438–457 (2010)
-
(2010)
Math. Oper. Res
, vol.35
, Issue.2
, pp. 438-457
-
-
Attouch, H.1
Bolte, J.2
Redont, P.3
Soubeyran, A.4
-
20
-
-
84885030988
-
A block coordinate descent method for regularized multiconvex optimization with applications to nonnegative tensor factorization and completion
-
Xu, Y., Yin, W.: A block coordinate descent method for regularized multiconvex optimization with applications to nonnegative tensor factorization and completion. SIAM J. Imaging Sci. 6(3), 1758–1789 (2013)
-
(2013)
SIAM J. Imaging Sci
, vol.6
, Issue.3
, pp. 1758-1789
-
-
Xu, Y.1
Yin, W.2
-
21
-
-
84906337892
-
Proximal alternating linearized minimization for nonconvex and nonsmooth problems
-
Bolte, J., Sabach, S., Teboulle, M.: Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math. Programm. 15, 1–36 (2013)
-
(2013)
Math. Programm
, vol.15
, pp. 1-36
-
-
Bolte, J.1
Sabach, S.2
Teboulle, M.3
-
23
-
-
84894098011
-
A proximal alternating linearization method for nonconvex optimization problems
-
Li, D., Pang, L.P., Chen, S.: A proximal alternating linearization method for nonconvex optimization problems. Optim. Methods Softw. 29(4), 646–657 (2014)
-
(2014)
Optim. Methods Softw
, vol.29
, Issue.4
, pp. 646-657
-
-
Li, D.1
Pang, L.P.2
Chen, S.3
-
24
-
-
35348955638
-
Clarke subgradients of stratifiable functions
-
Bolte, J., Daniilidis, A., Lewis, A., Shiota, M.: Clarke subgradients of stratifiable functions. SIAM J. Optim. 18(2), 556–572 (2007)
-
(2007)
SIAM J. Optim
, vol.18
, Issue.2
, pp. 556-572
-
-
Bolte, J.1
Daniilidis, A.2
Lewis, A.3
Shiota, M.4
-
25
-
-
84929309969
-
Tame topology and o-minimal structures
-
van den Dries, L.: Tame topology and o-minimal structures. Bull. AMS 37(3), 351–357 (2000)
-
(2000)
Bull. AMS
, vol.37
, Issue.3
, pp. 351-357
-
-
van den Dries, L.1
-
26
-
-
0000274906
-
Geometric categories and o-minimal structures
-
van den Dries, L., Miller, C.: Geometric categories and o-minimal structures. Duke Math. J. 84, 497–540 (1996)
-
(1996)
Duke Math. J
, vol.84
, pp. 497-540
-
-
van den Dries, L.1
Miller, C.2
-
27
-
-
79951577859
-
The Łojasiewicz gradient inequality in the infinite dimensional Hilbert space framework
-
Haraux, A., Jendoubi, M.A.: The Łojasiewicz gradient inequality in the infinite dimensional Hilbert space framework. J. Funct. Anal. 260(9), 2826–2842 (2010)
-
(2010)
J. Funct. Anal
, vol.260
, Issue.9
, pp. 2826-2842
-
-
Haraux, A.1
Jendoubi, M.A.2
-
28
-
-
77249105595
-
The Łojasiewicz–Simon gradient inequality in Hilbert spaces
-
Chill, R.: The Łojasiewicz–Simon gradient inequality in Hilbert spaces. In: Jendoubi, M.A. (ed.) Proceedings of the 5th European-Maghrebian Workshop on Semigroup Theory, Evolution Equations, and Applications, pp. 25–36 (2006)
-
(2006)
Jendoubi, M.A. (ed.) Proceedings of the 5th European-Maghrebian Workshop on Semigroup Theory, Evolution Equations, and Applications
, pp. 25-36
-
-
Chill, R.1
-
29
-
-
20244370379
-
-
Springer, NewYork:
-
Attouch, H., Buttazo, G., Michaille, G.: Variational Analysis in Sobolev and BV Spaces. MPS-SIAM Series on Optimization. Springer, NewYork (2008)
-
(2008)
Variational Analysis in Sobolev and BV Spaces. MPS-SIAM Series on Optimization
-
-
Attouch, H.1
Buttazo, G.2
Michaille, G.3
-
31
-
-
0016985417
-
Monotone operators and the proximal point algorithm
-
Rockafellar, R.T.: Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14(5), 877–898 (1976)
-
(1976)
SIAM J. Control Optim
, vol.14
, Issue.5
, pp. 877-898
-
-
Rockafellar, R.T.1
-
32
-
-
34249925266
-
Finite termination of the proximal point algorithm
-
Ferris, M.: Finite termination of the proximal point algorithm. Math. Program. 50, 359–366 (1991)
-
(1991)
Math. Program
, vol.50
, pp. 359-366
-
-
Ferris, M.1
-
33
-
-
67949118819
-
Asymptotic convergence to the optimal value of diagonal proximal iterations in convex minimization
-
Peypouquet, J.: Asymptotic convergence to the optimal value of diagonal proximal iterations in convex minimization. J. Convex Anal. 16(1), 277–286 (2009)
-
(2009)
J. Convex Anal
, vol.16
, Issue.1
, pp. 277-286
-
-
Peypouquet, J.1
-
34
-
-
33746537301
-
Convergence and decay rate to equilibrium of bounded solutions of quasilinear parabolic equations
-
Chill, R., Fiorenza, A.: Convergence and decay rate to equilibrium of bounded solutions of quasilinear parabolic equations. J. Differ. Equ. 228, 611–632 (2006)
-
(2006)
J. Differ. Equ
, vol.228
, pp. 611-632
-
-
Chill, R.1
Fiorenza, A.2
-
35
-
-
0000478038
-
Méthode générale pour la résolution des systèmes d’équations simultanées
-
Cauchy, A.-L.: Méthode générale pour la résolution des systèmes d’équations simultanées. C. R. Acad. Sci. Paris 25, 536–538 (1847)
-
(1847)
C. R. Acad. Sci. Paris
, vol.25
, pp. 536-538
-
-
Cauchy, A.-L.1
-
37
-
-
51249180487
-
Produits infinis de résolvantes
-
Brézis, H., Lions, P.-L.: Produits infinis de résolvantes. Israel J. Math. 29(4), 329–345 (1978)
-
(1978)
Israel J. Math
, vol.29
, Issue.4
, pp. 329-345
-
-
Brézis, H.1
Lions, P.-L.2
-
38
-
-
0000345334
-
Splitting algorithms for the sum of two nonlinear operators
-
Lions, P.L., Mercier, B.: Splitting algorithms for the sum of two nonlinear operators. SIAM J. Numer. Anal. 16, 964–979 (1979)
-
(1979)
SIAM J. Numer. Anal
, vol.16
, pp. 964-979
-
-
Lions, P.L.1
Mercier, B.2
-
39
-
-
0000120615
-
Ergodic convergence to a zero of the sum of monotone operators in Hilbert space
-
Passty, G.: Ergodic convergence to a zero of the sum of monotone operators in Hilbert space. J. Math. Anal. Appl. 72(2), 383–390 (1979)
-
(1979)
J. Math. Anal. Appl
, vol.72
, Issue.2
, pp. 383-390
-
-
Passty, G.1
-
40
-
-
16244413961
-
Hessian Riemannian gradient flows in convex programming
-
Alvarez, F., Bolte, J., Brahic, O.: Hessian Riemannian gradient flows in convex programming. SIAM J. Control Optim. 43(2), 477–501 (2004)
-
(2004)
SIAM J. Control Optim
, vol.43
, Issue.2
, pp. 477-501
-
-
Alvarez, F.1
Bolte, J.2
Brahic, O.3
-
41
-
-
77955575625
-
Interior proximal algorithm with variable metric for second-order cone programming: applications to structural optimization and support vector machines
-
Alvarez, F., López, J., Ramírez, H.: Interior proximal algorithm with variable metric for second-order cone programming: applications to structural optimization and support vector machines. Optim. Methods Softw. 25(4–6), 859–881 (2010)
-
(2010)
Optim. Methods Softw
, vol.25
, Issue.4-6
, pp. 859-881
-
-
Alvarez, F.1
López, J.2
Ramírez, H.3
-
42
-
-
79957473461
-
A continuous dynamical Newton-like approach to solving monotone inclusions
-
Attouch, H., Svaiter, B.F.: A continuous dynamical Newton-like approach to solving monotone inclusions. SIAM J. Optim. 49(2), 574–598 (2011)
-
(2011)
SIAM J. Optim
, vol.49
, Issue.2
, pp. 574-598
-
-
Attouch, H.1
Svaiter, B.F.2
-
43
-
-
84864687560
-
-
MIT Press, Cambridge:
-
Sra, S., Nowozin, S., Wright, S.J.: Optimization for Machine Learning. MIT Press, Cambridge (2011)
-
(2011)
Optimization for Machine Learning
-
-
Sra, S.1
Nowozin, S.2
Wright, S.J.3
-
44
-
-
0021522309
-
Two-metric projection methods for constrained optimization
-
Gafni, E.M., Bertsekas, D.P.: Two-metric projection methods for constrained optimization. SIAM J. Control Optim. 22(6), 936–964 (1984)
-
(1984)
SIAM J. Control Optim
, vol.22
, Issue.6
, pp. 936-964
-
-
Gafni, E.M.1
Bertsekas, D.P.2
-
45
-
-
0000377218
-
Projected Newton methods for optimization problems with simple constraints
-
Bertsekas, D.P.: Projected Newton methods for optimization problems with simple constraints. SIAM J. Control Optim. 20(2), 221–246 (1982)
-
(1982)
SIAM J. Control Optim
, vol.20
, Issue.2
, pp. 221-246
-
-
Bertsekas, D.P.1
-
46
-
-
70349387487
-
Local linear convergence for alternating and averaged non convex projections
-
Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged non convex projections. Found. Comput. Math. 9(4), 485–513 (2009)
-
(2009)
Found. Comput. Math
, vol.9
, Issue.4
, pp. 485-513
-
-
Lewis, A.S.1
Luke, D.R.2
Malick, J.3
-
47
-
-
33646365077
-
For most Large underdetermined systems of linear equations the minimal (formula presented)-norm solution is also the sparsest solution
-
Donoho, D.L.: For most Large underdetermined systems of linear equations the minimal $$\ell ^1$$ℓ1-norm solution is also the sparsest solution. Commun. Pure Appl. Math. 6, 59, 797–829 (2006)
-
(2006)
Commun. Pure Appl. Math. 6
, vol.59
, pp. 797-829
-
-
Donoho, D.L.1
-
48
-
-
77950517814
-
Counting the faces of randomly-projected hypercubes and orthants, with applications
-
Donoho, D.L., Tanner, J.: Counting the faces of randomly-projected hypercubes and orthants, with applications. Discret. Comput. Geom. 43, 522–541 (2010)
-
(2010)
Discret. Comput. Geom
, vol.43
, pp. 522-541
-
-
Donoho, D.L.1
Tanner, J.2
-
49
-
-
7044231546
-
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
-
Daubechies, I., Defrise, M., De Mol, C.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57(11), 1413–1457 (2004)
-
(2004)
Commun. Pure Appl. Math
, vol.57
, Issue.11
, pp. 1413-1457
-
-
Daubechies, I.1
Defrise, M.2
De Mol, C.3
-
50
-
-
79960591511
-
Rank-sparsity incoherence for matrix decomposition
-
Chandrasekaran, V., Sanghavi, S., Parillo, P.A., Willsky, A.S.: Rank-sparsity incoherence for matrix decomposition. SIAM J. Optim. 21(2), 572–596 (2011)
-
(2011)
SIAM J. Optim
, vol.21
, Issue.2
, pp. 572-596
-
-
Chandrasekaran, V.1
Sanghavi, S.2
Parillo, P.A.3
Willsky, A.S.4
-
51
-
-
77951126761
-
Fast algorithms for recovering a corrupted low-rank matrix
-
Ganesh, A., Lin, Z., Wright, J., Wu, L., Chen, M., Ma, Y.: Fast algorithms for recovering a corrupted low-rank matrix. In: Proceedings of the 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), pp. 213–216 (2009)
-
(2009)
Proceedings of the 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)
, pp. 213-216
-
-
Ganesh, A.1
Lin, Z.2
Wright, J.3
Wu, L.4
Chen, M.5
Ma, Y.6
-
52
-
-
84881306037
-
Sparse and low-rank matrix decomposition via alternating direction method
-
Yuan, X., Yang, J.: Sparse and low-rank matrix decomposition via alternating direction method. Pac. J. Optim. 9(1), 167–180 (2013)
-
(2013)
Pac. J. Optim
, vol.9
, Issue.1
, pp. 167-180
-
-
Yuan, X.1
Yang, J.2
-
53
-
-
78549288866
-
Guaranteed minimum rank solutions to linear matrix equations via nuclear norm minimization
-
Recht, B., Fazel, B., Parillo, P.A.: Guaranteed minimum rank solutions to linear matrix equations via nuclear norm minimization. SIAM Rev. 52, 471–501 (2007)
-
(2007)
SIAM Rev
, vol.52
, pp. 471-501
-
-
Recht, B.1
Fazel, B.2
Parillo, P.A.3
-
54
-
-
34548480020
-
A method for solving the convex programming problem with convergence rate O(formula presented)
-
Nesterov, Y.E.: A method for solving the convex programming problem with convergence rate O($$1/k^2$$1/k2). Dokl. Akad. Nauk SSSR 269, 543–547 (1983)
-
(1983)
Dokl. Akad. Nauk SSSR
, vol.269
, pp. 543-547
-
-
Nesterov, Y.E.1
-
55
-
-
85014561619
-
A fast iterative shrinkage-thresholding algorithm for linear inverse problems
-
Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2, 183–202 (2009)
-
(2009)
SIAM J. Imaging Sci
, vol.2
, pp. 183-202
-
-
Beck, A.1
Teboulle, M.2
-
56
-
-
78650786262
-
Gradient-based algorithms with applications in signal recovery problems
-
Palomar D, Eldar Y, (eds), Cambridge University Press, Cambridge:
-
Beck, A., Teboulle, M.: Gradient-based algorithms with applications in signal recovery problems. In: Palomar, D., Eldar, Y. (eds.) Convex Optimization in Signal Processing and Communications, pp. 33–88. Cambridge University Press, Cambridge (2010)
-
(2010)
Convex Optimization in Signal Processing and Communications
, pp. 33-88
-
-
Beck, A.1
Teboulle, M.2
-
57
-
-
84928817230
-
-
Ochs, P., Chen, Y., Brox, T.: Pock, T.: iPiano: Inertial Proximal Algorithm for Non-convex Optimization (2014). http://lmb.informatik.uni-freiburg.de/Publications/2014/OB14/
-
(2014)
Piano: Inertial Proximal Algorithm for Non-convex Optimization
-
-
Ochs, P.1
Chen, Y.2
Brox, T.3
Pock, T.4
-
58
-
-
84869162601
-
Approximation of sparse controls in semilinear equations by piecewise linear functions
-
Casas, E., Herzog, R., Wachsmuth, G.: Approximation of sparse controls in semilinear equations by piecewise linear functions. Numer. Math. 122(4), 645–669 (2012)
-
(2012)
Numer. Math
, vol.122
, Issue.4
, pp. 645-669
-
-
Casas, E.1
Herzog, R.2
Wachsmuth, G.3
|