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Complexity of partially separable convexly constrained optimization with non-Lipschitzian singularities. (English) Zbl 1411.90318

MSC:
90C30 Nonlinear programming
90C46 Optimality conditions and duality in mathematical programming
65K05 Numerical mathematical programming methods
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[1] W. Bian and X. Chen, and Y. Ye, Complexity analysis of interior point algorithms for non-Lipschitz and nonconvex minimization, Math. Program., 149 (2015), pp. 301–327. · Zbl 1318.90075
[2] E. G. Birgin, J. L. Gardenghi, J. M. Martínez, S. A. Santos, and Ph. L. Toint, Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models, Math. Program., 163 (2017), pp. 359–368. · Zbl 1365.90236
[3] C. Cartis, N. I. M. Gould, and Ph. L. Toint, On the complexity of steepest descent, Newton’s and regularized Newton’s methods for nonconvex unconstrained optimization, SIAM J. Optim., 20 (2010), pp. 2833–2852. · Zbl 1211.90225
[4] C. Cartis, N. I. M. Gould, and Ph. L. Toint, Adaptive cubic overestimation methods for unconstrained optimization. Part II: Worst-case function-evaluation complexity, Math. Program., 130 (2011), pp. 295–319. · Zbl 1229.90193
[5] C. Cartis, N. I. M. Gould, and Ph. L. Toint, An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity, IMA J. Numer. Anal., 32 (2012), pp. 1662–1695. · Zbl 1267.65061
[6] C. Cartis, N. I. M. Gould, and Ph. L. Toint, Universal Regularization Methods: Varying the Power, the Smoothness and the Accuracy, Technical report naXys-7-2016, Namur Center for Complex Systems, University of Namur, Namur, Belgium, 2016. · Zbl 1436.90136
[7] X. Chen, D. Ge, Z. Wang, and Y. Ye, Complexity of unconstrained \(ℓ_2\)-\(ℓ_p\) minimization, Math. Program., 143 (2014), pp. 371–383. · Zbl 1285.90039
[8] X. Chen, L. Niu, and Y. Yuan, Optimality conditions and smoothing trust region Newton method for nonLipschitz optimization, SIAM J. Optim., 23 (2013), pp. 1528–1552. · Zbl 1291.90238
[9] X. Chen, F. Xu, and Y. Ye, Lower bound theory of nonzero entries in solutions of \(ℓ_2\)-\(ℓ_p\) minimization, SIAM J. Sci. Comput., 32 (2010), pp. 2832–2852. · Zbl 1242.90174
[10] A. R. Conn, N. I. M. Gould, A. Sartenaer, and Ph. L. Toint, Convergence properties of minimization algorithms for convex constraints using a structured trust region, SIAM J. Optim., 6 (1996), pp. 1059–1086. · Zbl 0868.90106
[11] A. R. Conn, N. I. M. Gould, and Ph. L. Toint, LANCELOT: A Fortran Package for Large-Scale Nonlinear Optimization (Release A), Springer Ser. Comput. Math. 17, Springer, Berlin, 1992. · Zbl 0761.90087
[12] A. R. Conn, N. I. M. Gould, and Ph. L. Toint, Trust-Region Methods, MPS-SIAM Ser. Optim., SIAM, Philadelphia, PA, 2000.
[13] R. Fourer, D. M. Gay, and B. W. Kernighan, AMPL: A Mathematical Programming Language, Computer science technical report, AT&T Bell Laboratories, Murray Hill, NJ, 1987. · Zbl 0701.90062
[14] D. M. Gay, Automatically Finding and Exploiting Partially Separable Structure in Nonlinear Programming Problems, Technical report, Bell Laboratories, Murray Hill, NJ, 1996.
[15] D. Goldfarb and S. Wang, Partial-update Newton methods for unary, factorable and partially separable optimization, SIAM J. Optim., 3 (1993), pp. 382–397. · Zbl 0784.90075
[16] N. I. M. Gould, J. Hogg, T. Rees, and J. Scott, Solving Nonlinear Least-Squares Problems, Technical report, Rutherford Appleton Laboratory, Chilton, UK, 2016.
[17] N. I. M. Gould, D. Orban, and Ph. L. Toint, \sf CUTEst: A constrained and unconstrained testing environment with safe threads for mathematical optimization, Comput. Optim. Appl., 60 (2015), pp. 545–557. · Zbl 1325.90004
[18] N. I. M. Gould and Ph. L. Toint, \sf FILTRANE, a Fortran 95 filter-trust-region package for solving systems of nonlinear equalities, nonlinear inequalities and nonlinear least-squares problems, ACM Trans. Math. Software, 33 (2007), pp. 3–25.
[19] G. Grapiglia and Yu. Nesterov, Regularized Newton methods for minimizing functions with Hölder continuous Hessians, SIAM J. Optim., 27 (2017), pp. 478–506. · Zbl 1406.49029
[20] A. Griewank, The Modification of Newton’s Method for Unconstrained Optimization by Bounding Cubic Terms, Technical report NA/12, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, 1981.
[21] A. Griewank and Ph. L. Toint, On the unconstrained optimization of partially separable functions, in Nonlinear Optimization 1981, M. J. D. Powell, ed., Academic Press, London, 1982, pp. 301–312. · Zbl 0563.90085
[22] J. Huang, J. L. Horowitz, and S. Ma, Asymptotic properties of bridge estimators in sparse high-dimensional regression models, Ann. Statist., 36 (2018), pp. 587–613. · Zbl 1133.62048
[23] Y. F. Liu, S. Ma, Y. H. Dai, and S. Zhang, A smoothing SQP framework for a class of composite \(L_q\) minimization over polyhedron, Math. Program., 158 (2016), pp. 467–500. · Zbl 1346.90684
[24] J. Mareček, P. Richtárik, and M. Takáč, Distributed Block Coordinate Descent for Minimizing Partially Separable Functions, Technical report, Department of Mathematics and Statistics, University of Edinburgh, Edinburgh, 2014. · Zbl 1330.65089
[25] J. M. Martínez, On high-order model regularization for constrained optimization, SIAM J. Optim., 27 (2017), pp. 2447–2458. · Zbl 1387.90200
[26] Yu. Nesterov and B. T. Polyak, Cubic regularization of Newton method and its global performance, Math. Program., 108 (2006), pp. 177–205. · Zbl 1142.90500
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