From error bounds to the complexity of first-order descent methods for convex functions
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Bruce W. Suter | Juan Peypouquet | Jérôme Bolte | Trong Phong Nguyen | J. Bolte | J. Peypouquet | B. Suter | T. P. Nguyen
[1] A. Hoffman. On approximate solutions of systems of linear inequalities , 1952 .
[2] L. Kantorovich,et al. Functional analysis in normed spaces , 1952 .
[3] S. Łojasiewicz. Sur le problème de la division , 1959 .
[4] H. Brezis. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert , 1973 .
[5] S. M. Robinson. An Application of Error Bounds for Convex Programming in a Linear Space , 1975 .
[6] Ronald E. Bruck. Asymptotic convergence of nonlinear contraction semigroups in Hilbert space , 1975 .
[7] R. Rockafellar. Monotone Operators and the Proximal Point Algorithm , 1976 .
[8] 丸山 徹. Convex Analysisの二,三の進展について , 1977 .
[9] Olvi L. Mangasarian,et al. A Condition Number for Differentiable Convex Inequalities , 1985, Math. Oper. Res..
[10] Alfred Auslender,et al. Global Regularity Theorems , 1988, Math. Oper. Res..
[11] Michael C. Ferris,et al. Finite termination of the proximal point algorithm , 1991, Math. Program..
[12] J. Dedieu. Penalty functions in subanalytic optimization , 1992 .
[13] Marie-Françoise Roy,et al. Real algebraic geometry , 1992 .
[14] S. Łojasiewicz. Sur la géométrie semi- et sous- analytique , 1993 .
[15] Z.-Q. Luo,et al. Error bounds and convergence analysis of feasible descent methods: a general approach , 1993, Ann. Oper. Res..
[16] M. Ferris,et al. Weak sharp minima in mathematical programming , 1993 .
[17] Zhi-Quan Luo,et al. Error bounds for analytic systems and their applications , 1994, Math. Program..
[18] Zhi-Quan Luo,et al. Extension of Hoffman's Error Bound to Polynomial Systems , 1994, SIAM J. Optim..
[19] Patrick L. Combettes,et al. Inconsistent signal feasibility problems: least-squares solutions in a product space , 1994, IEEE Trans. Signal Process..
[20] Heinz H. Bauschke,et al. On Projection Algorithms for Solving Convex Feasibility Problems , 1996, SIAM Rev..
[21] O. Cornejo,et al. Conditioning and Upper-Lipschitz Inverse Subdifferentials in Nonsmooth Optimization Problems , 1997 .
[22] Jong-Shi Pang,et al. Error bounds in mathematical programming , 1997, Math. Program..
[23] K. Kurdyka. On gradients of functions definable in o-minimal structures , 1998 .
[24] Marie-Françoise Roy,et al. Witt Rings in Real Algebraic Geometry , 1998 .
[25] Z. Luo,et al. Error Bounds for Quadratic Systems , 1999 .
[26] Xi Yin Zheng,et al. Global error bounds with fractional exponents , 2000, Math. Program..
[27] D. Bertsekas,et al. Convergen e Rate of In remental Subgradient Algorithms , 2000 .
[28] M. Coste. AN INTRODUCTION TO O-MINIMAL GEOMETRY , 2002 .
[29] Diethard Klatte,et al. A Frank–Wolfe Type Theorem for Convex Polynomial Programs , 2002, Comput. Optim. Appl..
[30] Constantin Zualinescu. Sharp Estimates for Hoffman's Constant for Systems of Linear Inequalities and Equalities , 2003, SIAM J. Optim..
[31] I. Daubechies,et al. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.
[32] Marc Teboulle,et al. Convergence rate analysis and error bounds for projection algorithms in convex feasibility problems , 2003, Optim. Methods Softw..
[33] Patrick L. Combettes,et al. Signal Recovery by Proximal Forward-Backward Splitting , 2005, Multiscale Model. Simul..
[34] Robert E. Mahony,et al. Convergence of the Iterates of Descent Methods for Analytic Cost Functions , 2005, SIAM J. Optim..
[35] F. Giannessi. Variational Analysis and Generalized Differentiation , 2006 .
[36] B. Mordukhovich. Variational analysis and generalized differentiation , 2006 .
[37] Adrian S. Lewis,et al. The [barred L]ojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems , 2006, SIAM J. Optim..
[38] Adrian S. Lewis,et al. Clarke Subgradients of Stratifiable Functions , 2006, SIAM J. Optim..
[39] J. Peypouquet. ASYMPTOTIC CONVERGENCE TO THE OPTIMAL VALUE OF DIAGONAL PROXIMAL ITERATIONS IN CONVEX MINIMIZATION , 2008 .
[40] Jean-Noël Corvellec,et al. Nonlinear error bounds for lower semicontinuous functions on metric spaces , 2008, Math. Program..
[41] E.J. Candes,et al. An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.
[42] Marc Teboulle,et al. A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..
[43] J. Bolte,et al. Characterizations of Lojasiewicz inequalities: Subgradient flows, talweg, convexity , 2009 .
[44] Hédy Attouch,et al. On the convergence of the proximal algorithm for nonsmooth functions involving analytic features , 2008, Math. Program..
[45] Hédy Attouch,et al. Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Lojasiewicz Inequality , 2008, Math. Oper. Res..
[46] Heinz H. Bauschke,et al. Convex Analysis and Monotone Operator Theory in Hilbert Spaces , 2011, CMS Books in Mathematics.
[47] Patrick L. Combettes,et al. Proximal Splitting Methods in Signal Processing , 2009, Fixed-Point Algorithms for Inverse Problems in Science and Engineering.
[48] P. L. Combettes,et al. There is no variational characterization of the cycles in the method of periodic projections , 2011, 1102.1378.
[49] Benar Fux Svaiter,et al. Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods , 2013, Math. Program..
[50] Guoyin Li,et al. Global error bounds for piecewise convex polynomials , 2013, Math. Program..
[51] Hà Huy Vui. Global Hölderian Error Bound for Nondegenerate Polynomials , 2013, SIAM J. Optim..
[52] P. Vuong. New Fractional Error Bounds for Polynomial Systems with Applications to Holderian Stability in Optimization and Spectral Theory of Tensors , 2014 .
[53] Mohamed-Jalal Fadili,et al. Local Linear Convergence of Forward-Backward under Partial Smoothness , 2014, NIPS.
[54] Marc Teboulle,et al. Proximal alternating linearized minimization for nonconvex and nonsmooth problems , 2013, Mathematical Programming.
[55] J. Peypouquet. Convex Optimization in Normed Spaces: Theory, Methods and Examples , 2015 .
[56] Juan Peypouquet,et al. Splitting Methods with Variable Metric for Kurdyka–Łojasiewicz Functions and General Convergence Rates , 2015, J. Optim. Theory Appl..
[57] Boris S. Mordukhovich,et al. New fractional error bounds for polynomial systems with applications to Hölderian stability in optimization and spectral theory of tensors , 2015, Math. Program..
[58] J. Bolte,et al. On damped second-order gradient systems , 2014, 1411.8005.
[59] J. Peypouquet. Convex Optimization in Normed Spaces , 2015 .
[60] Edouard Pauwels,et al. Majorization-Minimization Procedures and Convergence of SQP Methods for Semi-Algebraic and Tame Programs , 2014, Math. Oper. Res..
[61] Edouard Pauwels. The value function approach to convergence analysis in composite optimization , 2016, Oper. Res. Lett..
[62] Shimrit Shtern,et al. Linearly convergent away-step conditional gradient for non-strongly convex functions , 2015, Mathematical Programming.
[63] Boris S. Mordukhovich,et al. Error bounds for parametric polynomial systems with applications to higher-order stability analysis and convergence rates , 2015, Math. Program..