메뉴 건너뛰기




Volumn 4, Issue , 2014, Pages 807-827

A review on subspace methods for nonlinear optimization

Author keywords

Nonlinear optimization; Numerical methods; Subproblems; Subspace techniques

Indexed keywords

CONSTRAINED OPTIMIZATION; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; NONLINEAR PROGRAMMING; NUMERICAL METHODS;

EID: 84973258090     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper
Times cited : (32)

References (42)
  • 2
  • 3
    • 0033296256 scopus 로고    scopus 로고
    • A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems
    • M.A. Branch, T.F. Coleman, and Y.Y. Li, A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems, SIAM J. Sci. Comput. 21 (2007), 1-23.
    • (2007) SIAM J. Sci. Comput , vol.21 , pp. 1-23
    • Branch, M.A.1    Coleman, T.F.2    Li, Y.Y.3
  • 5
    • 80051762104 scopus 로고    scopus 로고
    • Distributed optimization and statistical learning via the alternating direction method of multipliers
    • S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers, Foundations and Trends in Machine Learning 3 (2011), 1-122
    • (2011) Foundations and Trends in Machine Learning , vol.3 , pp. 1-122
    • Boyd, S.1    Parikh, N.2    Chu, E.3    Peleato, B.4    Eckstein, J.5
  • 6
    • 84944621308 scopus 로고    scopus 로고
    • On effciently combining limited memory and trust-region techniques
    • Report, AMSS, CAS
    • O. Burdakov, L.J. Gong, Y.X. Yuan, and S. Zikrin, On effciently combining limited memory and trust-region techniques, Report, AMSS, CAS, 2013.
    • (2013)
    • Burdakov, O.1    Gong, L.J.2    Yuan, Y.X.3    Zikrin, S.4
  • 7
    • 0002336672 scopus 로고
    • A trust region algorithm for nonlinear equality constrained optimization
    • P.T. Boggs, R.H. Byrd, and R.B. Schnabel, eds., (SIAM, Philadelphia)
    • Celis, M.R., Dennis, J.E., and Tapia, R.A., A trust region algorithm for nonlinear equality constrained optimization, in: P.T. Boggs, R.H. Byrd, and R.B. Schnabel, eds., Numerical Optimization (SIAM, Philadelphia, 1985), 71-82.
    • (1985) Numerical Optimization , pp. 71-82
    • Celis, M.R.1    Dennis, J.E.2    Tapia, R.A.3
  • 8
    • 0030303844 scopus 로고    scopus 로고
    • An interior point trust region approach for nonlinear minimization subject to bounds
    • T. Coleman and Y.Y. Li, An interior point trust region approach for nonlinear minimization subject to bounds, SIAM J. Optimization 6 (1996), 418-445.
    • (1996) SIAM J. Optimization , vol.6 , pp. 418-445
    • Coleman, T.1    Li, Y.Y.2
  • 11
    • 35148813504 scopus 로고    scopus 로고
    • Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization
    • M. Elad, B. Matalon, and M. Zibulevsky, Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization, Appl. Comput. Harmon. Anal. 23 (2007) 346-367
    • (2007) Appl. Comput. Harmon. Anal , vol.23 , pp. 346-367
    • Elad, M.1    Matalon, B.2    Zibulevsky, M.3
  • 12
    • 0040133819 scopus 로고
    • Second order correction for nondifferentiable optimization
    • G.A. Watson, ed., Springer-Verlag, Berlin
    • R. Fletcher, Second order correction for nondifferentiable optimization, in: G.A. Watson, ed., Numerical Analysis, Springer-Verlag, Berlin, (1982), 85-115.
    • (1982) Numerical Analysis , pp. 85-115
    • Fletcher, R.1
  • 13
    • 0036344538 scopus 로고    scopus 로고
    • Reduced-Hessian quasi-Newton methods for unconstrained optimization
    • P.E. Gill and M.W. Leonard, Reduced-Hessian quasi-Newton methods for unconstrained optimization, SIAM J. Optim. 1 (2001), 209-237.
    • (2001) SIAM J. Optim , vol.1 , pp. 209-237
    • Gill, P.E.1    Leonard, M.W.2
  • 15
    • 84939607223 scopus 로고
    • North-Holland Publishing Co., Amsterdam, Applications to the numerical solution of boundary value problems, Translated from the French by B. Hunt and D. C. Spicer
    • M. Fortin and R. Glowinski, Augmented Lagrangian Methods, Vol. 15 of Studies in Mathematics and its Applications, North-Holland Publishing Co., Amsterdam, 1983. Applications to the numerical solution of boundary value problems, Translated from the French by B. Hunt and D. C. Spicer.
    • (1983) Augmented Lagrangian Methods, Vol. 15 of Studies in Mathematics and its Applications
    • Fortin, M.1    Glowinski, R.2
  • 16
    • 0003887107 scopus 로고
    • Augmented Lagrangian and Operator-splitting Methods in Nonlinear Mechanics
    • of SIAM Studies in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
    • R. Glowinski and P. Le Tallec, Augmented Lagrangian and Operator-splitting Methods in Nonlinear Mechanics, Vol. 9 of SIAM Studies in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1989.
    • (1989) , vol.9
    • Glowinski, R.1    Le Tallec, P.2
  • 17
    • 19844363263 scopus 로고    scopus 로고
    • Numerical methods for large-scale nonlinear optimization
    • N.I.M. Gould, D. Orban, and Ph.L. Toint, Numerical methods for large-scale nonlinear optimization, Acta Numerica (2005), 299-361.
    • (2005) Acta Numerica , pp. 299-361
    • Gould, N.I.M.1    Orban, D.2    Toint, Ph.L.3
  • 18
    • 84899108794 scopus 로고    scopus 로고
    • A subspace version of the Powell-Yuan trust-region algorithm for equality constrained optimization
    • Grapiglia, G.N., Yuan, J.Y., and Yuan, Y.X., A subspace version of the Powell-Yuan trust-region algorithm for equality constrained optimization, J. Operations Research Society of China 1 (2013), 425- 451.
    • (2013) J. Operations Research Society of China , vol.1 , pp. 425-451
    • Grapiglia, G.N.1    Yuan, J.Y.2    Yuan, Y.X.3
  • 19
    • 0036223489 scopus 로고    scopus 로고
    • Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method
    • A. V. Knyazev, Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method, SIAM J. Sci. Comput. 23 (2001), 517-541.
    • (2001) SIAM J. Sci. Comput , vol.23 , pp. 517-541
    • Knyazev, A. V.1
  • 21
    • 33646887390 scopus 로고
    • On the limited memory BFGS method for large scale optimization
    • D.C. Liu and J. Nocedal, On the limited memory BFGS method for large scale optimization, Mathematical Programming 45 (1989), 503-528.
    • (1989) Mathematical Programming , vol.45 , pp. 503-528
    • Liu, D.C.1    Nocedal, J.2
  • 22
    • 84904008585 scopus 로고    scopus 로고
    • On the convergence of the self-consistent field iteration in Kohn-Sham density function theory
    • accepted by
    • X. Liu, X. Wang, Z.W. Wen, and Y.X. Yuan, On the convergence of the self-consistent field iteration in Kohn-Sham density function theory, accepted by SIAM Journal on Matrix Analysis and Applications (2014).
    • (2014) SIAM Journal on Matrix Analysis and Applications
    • Liu, X.1    Wang, X.2    Wen, Z.W.3    Yuan, Y.X.4
  • 23
    • 84884952807 scopus 로고    scopus 로고
    • Limited memory block Krylov subspace optimization for computing dominant singular value decompositions
    • X. Liu, Z.W. Wen and Y. Zhang, Limited memory block Krylov subspace optimization for computing dominant singular value decompositions, SIAM Journal on Scientific Computing 35 (2013), A1641-A1668
    • (2013) SIAM Journal on Scientific Computing , vol.35 , pp. A1641-A1668
    • Liu, X.1    Wen, Z.W.2    Zhang, Y.3
  • 24
    • 77956506829 scopus 로고    scopus 로고
    • Coordinate descent optimization for '1 minimization with application to compressed sensing; a greedy algorithm
    • Y.Y. Li and S. Osher, Coordinate descent optimization for '1 minimization with application to compressed sensing; a greedy algorithm, Inverse Probl. Imaging 3 (2009), 487-503
    • (2009) Inverse Probl. Imaging , vol.3 , pp. 487-503
    • Li, Y.Y.1    Osher, S.2
  • 25
    • 0026678659 scopus 로고
    • On the convergence of the coordinate descent method for convex differentiable minimization
    • Z. Q. Luo and P. Tseng, On the convergence of the coordinate descent method for convex differentiable minimization, J. Optim. Theory Appl. 72 (1992), 7-35
    • (1992) J. Optim. Theory Appl , vol.72 , pp. 7-35
    • Luo, Z. Q.1    Tseng, P.2
  • 26
    • 0002897657 scopus 로고
    • A superlinearly convergent algorithm for constrained optimization problems
    • D.Q. Mayne and E. Polak, A superlinearly convergent algorithm for constrained optimization problems, Math. Prog. Study 16 (1982), 45-61.
    • (1982) Math. Prog. Study , vol.16 , pp. 45-61
    • Mayne, D.Q.1    Polak, E.2
  • 27
    • 0031525729 scopus 로고    scopus 로고
    • A subspace limited memory quasi-Newton algorithm for largescale nonlinear bound constrained optimization
    • Q. Ni and Y.X. Yuan, A subspace limited memory quasi-Newton algorithm for largescale nonlinear bound constrained optimization, Mathematics of Computations 66 (1997), 1509-1520.
    • (1997) Mathematics of Computations , vol.66 , pp. 1509-1520
    • Ni, Q.1    Yuan, Y.X.2
  • 28
    • 34249955300 scopus 로고
    • A trust region algorithm for equality constrained optimization
    • M.J.D. Powell and Y.X. Yuan, A trust region algorithm for equality constrained optimization, Mathematical Programming 49 (1991), 189-211.
    • (1991) Mathematical Programming , vol.49 , pp. 189-211
    • Powell, M.J.D.1    Yuan, Y.X.2
  • 30
    • 70350370784 scopus 로고    scopus 로고
    • A geometric buildup algorithm for the solution of the distance geometry problem using least-squares approximation
    • A. Sit, Z.J. Wu, and Y.X. Yuan, A geometric buildup algorithm for the solution of the distance geometry problem using least-squares approximation, Bulletin of Mathematical Biology 71 (2009), 1914-1933.
    • (2009) Bulletin of Mathematical Biology , vol.71 , pp. 1914-1933
    • Sit, A.1    Wu, Z.J.2    Yuan, Y.X.3
  • 31
    • 21844503871 scopus 로고
    • A subspace study on conjugate gradient algorithms
    • J. Stoer and Y.X. Yuan, A subspace study on conjugate gradient algorithms, ZAMM Z. angew. Math. Mech. 75 (1995), 69-77.
    • (1995) ZAMM Z. angew. Math. Mech , vol.75 , pp. 69-77
    • Stoer, J.1    Yuan, Y.X.2
  • 33
    • 33846702780 scopus 로고    scopus 로고
    • A subspace trust region method for large scale unconstrained optimization
    • Y.X. Yuan eds. (Science Press, Beijing/NewYork)
    • Z.H. Wang, Z.W. Wen, and Y.X. Yuan, A subspace trust region method for large scale unconstrained optimization, in: Y.X. Yuan eds. Numerical Linear Algebra and Optimization (Science Press, Beijing/NewYork, 2004), pp. 265-274.
    • (2004) Numerical Linear Algebra and Optimization , pp. 265-274
    • Wang, Z.H.1    Wen, Z.W.2    Yuan, Y.X.3
  • 34
    • 33748852443 scopus 로고    scopus 로고
    • A subspace implementation of quasi-Newton trust region methods for unconstrained optimization
    • Z.H. Wang and Y.X. Yuan, A subspace implementation of quasi-Newton trust region methods for unconstrained optimization, Numerische Mathematik 104 (2006), 241-269.
    • (2006) Numerische Mathematik , vol.104 , pp. 241-269
    • Wang, Z.H.1    Yuan, Y.X.2
  • 36
    • 84884933952 scopus 로고    scopus 로고
    • Adaptive regularized selfconsistent field iteration with exact Hessian for electronic structure calculation
    • Z.W. Wen, A. Milzarek, M. Ulbrich, and H.C. Zhang, Adaptive regularized selfconsistent field iteration with exact Hessian for electronic structure calculation, SIAM Journal on Scientific Computing 35 (2013), pp. A1299-A1324.
    • (2013) SIAM Journal on Scientific Computing , vol.35 , pp. A1299-A1324
    • Wen, Z.W.1    Milzarek, A.2    Ulbrich, M.3    Zhang, H.C.4
  • 37
    • 79952297247 scopus 로고    scopus 로고
    • Alternating direction augmented Lagrangian methods for semidefinite programming
    • Z.W. Wen, D. Goldfarb, and W. Yin, Alternating direction augmented Lagrangian methods for semidefinite programming, Mathematical Programming Computation 2 (2010), 203-230
    • (2010) Mathematical Programming Computation , vol.2 , pp. 203-230
    • Wen, Z.W.1    Goldfarb, D.2    Yin, W.3
  • 38
    • 77955666600 scopus 로고    scopus 로고
    • A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization, and continuation
    • Z.W. Wen, W. Yin, D. Goldfarb, and Y. Zhang, A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization, and continuation, SIAM Journal on Scientific Computing 32 (2010), 1832-1857.
    • (2010) SIAM Journal on Scientific Computing , vol.32 , pp. 1832-1857
    • Wen, Z.W.1    Yin, W.2    Goldfarb, D.3    Zhang, Y.4
  • 39
    • 0036003411 scopus 로고    scopus 로고
    • Global and uniform convergence of subspace correction methods for some convex optimization problems
    • X.C. Tai and J.C. Xu, Global and uniform convergence of subspace correction methods for some convex optimization problems, Math. Comp. 71 (2002), 105-124.
    • (2002) Math. Comp , vol.71 , pp. 105-124
    • Tai, X.C.1    Xu, J.C.2
  • 40
    • 79952307213 scopus 로고    scopus 로고
    • Alternating direction algorithms for l1-problems in compressive sensing
    • J. Yang and Y. Zhang, Alternating direction algorithms for l1-problems in compressive sensing, SIAM journal on scientific computing 33 (2011), 250-278.
    • (2011) SIAM journal on scientific computing , vol.33 , pp. 250-278
    • Yang, J.1    Zhang, Y.2
  • 42
    • 84865662874 scopus 로고    scopus 로고
    • Subspace methods for large scale nonlinear equations and nonlinear least squares
    • Subspace methods for large scale nonlinear equations and nonlinear least squares, Optimization and Engineering 10 (2009), 207-218.
    • (2009) Optimization and Engineering , vol.10 , pp. 207-218


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.