메뉴 건너뛰기




Volumn 22, Issue 2, 2012, Pages 474-500

A sequential quadratic programming algorithm for nonconvex, nonsmooth constrained optimization

Author keywords

Constrained optimization; Exact penalization; Gradient sampling; Nonconvex optimization; Nonsmooth optimization; Sequential quadratic programming

Indexed keywords

EXACT PENALIZATION; GRADIENT SAMPLING; NONCONVEX OPTIMIZATION; NONSMOOTH OPTIMIZATION; SEQUENTIAL QUADRATIC PROGRAMMING;

EID: 84865690526     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/090780201     Document Type: Article
Times cited : (128)

References (43)
  • 1
    • 33645263538 scopus 로고    scopus 로고
    • A masked spectral bound for maximum-entropy sampling
    • A. di Bucchianico, H. Läuter, and H. P. Wynn, eds., Springer-Verlag, Berlin
    • K. M. Anstreicher and J. Lee, A masked spectral bound for maximum-entropy sampling, in MODA 7: Advances in Model-Oriented Design and Analysis, A. di Bucchianico, H. Läuter, and H. P. Wynn, eds., Springer-Verlag, Berlin, 2004, pp. 1-10.
    • (2004) MODA 7: Advances in Model-Oriented Design and Analysis , pp. 1-10
    • Anstreicher, K.M.1    Lee, J.2
  • 2
    • 0141712989 scopus 로고    scopus 로고
    • Robust optimization: Methodology and applications
    • A. Ben-Tal and A. Nemirovski, Robust optimization: Methodology and applications, Math. Program. Ser. B, 92 (2002), pp. 453-480.
    • (2002) Math. Program. Ser. B , vol.92 , pp. 453-480
    • Ben-Tal, A.1    Nemirovski, A.2
  • 3
    • 44649149897 scopus 로고
    • Sequential quadratic programming
    • P. T. Boggs and J. W. Tolle, Sequential quadratic programming, Acta Numer., 4 (1995), pp. 1-51.
    • (1995) Acta Numer. , vol.4 , pp. 1-51
    • Boggs, P.T.1    Tolle, J.W.2
  • 4
    • 0026190240 scopus 로고
    • An exact penalization viewpoint of constrained optimization
    • J. V. Burke, An exact penalization viewpoint of constrained optimization, SIAM J. Control Optim., 29 (1991), pp. 968-998.
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 968-998
    • Burke, J.V.1
  • 5
    • 0026118632 scopus 로고
    • Calmness and exact penalization
    • J. V. Burke, Calmness and exact penalization, SIAM J. Control Optim., 29 (1991), pp. 493- 497.
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 493-497
    • Burke, J.V.1
  • 7
    • 0036672502 scopus 로고    scopus 로고
    • Approximating subdifferentials by random sampling of gradients
    • J. V. Burke, A. S. Lewis, and M. L. Overton, Approximating subdifferentials by random sampling of gradients, Math. Oper. Res., 27 (2002), pp. 567-584. (Pubitemid 35019794)
    • (2002) Mathematics of Operations Research , vol.27 , Issue.3 , pp. 567-584
    • Burke, J.V.1    Lewis, A.S.2    Overton, M.L.3
  • 8
    • 23844446458 scopus 로고    scopus 로고
    • A robust gradient sampling algorithm for nonsmooth, nonconvex optimization
    • DOI 10.1137/030601296
    • J. V. Burke, A. S. Lewis, and M. L. Overton, A robust gradient sampling algorithm for nonsmooth, nonconvex optimization, SIAM J. Optim., 15 (2005), pp. 751-779. (Pubitemid 41156914)
    • (2005) SIAM Journal on Optimization , vol.15 , Issue.3 , pp. 751-779
    • Burke, J.V.1    Lewis, A.S.2    Overton, M.L.3
  • 9
    • 84862277033 scopus 로고    scopus 로고
    • A line search exact penalty method using steering rules
    • DOI: 10.1007/s10107-010-0408-0
    • R. H. Byrd, G. Lopez-Calva, and J. Nocedal, A line search exact penalty method using steering rules, Math. Program., DOI: 10.1007/s10107-010-0408-0.
    • Math. Program.
    • Byrd, R.H.1    Lopez-Calva, G.2    Nocedal, J.3
  • 10
    • 33947416035 scopus 로고    scopus 로고
    • Near-optimal signal recovery from random projections: Universal encoding strategies?
    • DOI 10.1109/TIT.2006.885507
    • E. J. Candès and T. Tao, Near optimal signal recovery from random projections: Universal encoding strategies, IEEE Trans. Inform. Theory, 52 (2006), pp. 5406-5425. (Pubitemid 46445381)
    • (2006) IEEE Transactions on Information Theory , vol.52 , Issue.12 , pp. 5406-5425
    • Candes, E.J.1    Tao, T.2
  • 11
    • 0003859933 scopus 로고
    • Optimization and nonsmooth analysis
    • John Wiley, New York
    • F. H. Clarke, Optimization and Nonsmooth Analysis, CMS Ser. Monogr. Adv. Texts, John Wiley, New York, 1983.
    • (1983) CMS Ser. Monogr. Adv. Texts
    • Clarke, F.H.1
  • 12
    • 84865677190 scopus 로고    scopus 로고
    • An adaptive gradient sampling algorithm for nonsmooth optimization
    • Lehigh ISE/COR@L Technical Report 11T-008, in review
    • F. E. Curtis and X. Que, An adaptive gradient sampling algorithm for nonsmooth optimization, Lehigh ISE/COR@L Technical Report 11T-008, Optim. Methods Softw., in review.
    • Optim. Methods Softw.
    • Curtis, F.E.1    Que, X.2
  • 16
    • 0025530751 scopus 로고
    • A successive quadratic programming method for a class of constrained nonsmooth optimization problems
    • M. Fukushima, A successive quadratic programming method for a class of constrained nonsmooth optimization problems, Math. Program., 49 (1990), pp. 231-251.
    • (1990) Math. Program. , vol.49 , pp. 231-251
    • Fukushima, M.1
  • 17
    • 84865680112 scopus 로고    scopus 로고
    • Sequential quadratic programming methods
    • Mixed Integer Nonlinear Programming, J. Lee and S. Leyffer, eds., Springer-Verlag, New York
    • P. E. Gill and E. Wong, Sequential quadratic programming methods, in Mixed Integer Nonlinear Programming, J. Lee and S. Leyffer, eds., IMA Vol. Math. Appl. 154, Springer-Verlag, New York, 2012, pp. 147-224.
    • (2012) IMA Vol. Math. Appl. , vol.154 , pp. 147-224
    • Gill, P.E.1    Wong, E.2
  • 18
    • 0038300035 scopus 로고    scopus 로고
    • Robust portfolio selection problems
    • D. Goldfarb and G. Iyengar, Robust portfolio selection problems, Math. Oper. Res., 28 (2003), pp. 1-38.
    • (2003) Math. Oper. Res. , vol.28 , pp. 1-38
    • Goldfarb, D.1    Iyengar, G.2
  • 21
    • 34250293137 scopus 로고
    • A globally convergent method for nonlinear programming
    • S. P. Han, A globally convergent method for nonlinear programming, J. Optim. Theory Appl., 22 (1977), pp. 297-309.
    • (1977) J. Optim. Theory Appl. , vol.22 , pp. 297-309
    • Han, S.P.1
  • 22
    • 34250270048 scopus 로고
    • Exact penalty functions in nonlinear programming
    • S. P. Han and O. L. Mangasarian, Exact penalty functions in nonlinear programming, Math. Program., 17 (1979), pp. 251-269. (Pubitemid 10439054)
    • (1979) Mathematical Programming , vol.17 , Issue.3 , pp. 251-269
    • Han, S.P.1    Mangasarian, O.L.2
  • 23
  • 24
    • 45749105960 scopus 로고    scopus 로고
    • A bundle-filter method for nonsmooth convex constrained optimization
    • E. W. Karas, A. Ribeiro, C. A. Sagastizábal, and M. V. Solodov, A bundle-filter method for nonsmooth convex constrained optimization, Math. Program., 116 (2007), pp. 297-320.
    • (2007) Math. Program. , vol.116 , pp. 297-320
    • Karas, E.W.1    Ribeiro, A.2    Sagastizábal, C.A.3    Solodov, M.V.4
  • 25
    • 77955578397 scopus 로고    scopus 로고
    • Limited memory bundle method for large bound constrained nonsmooth optimization: Convergence analysis
    • N. Karmitsa and M. M. Makela, Limited memory bundle method for large bound constrained nonsmooth optimization: Convergence analysis, Optim. Methods Softw., 25 (2010), pp. 895-916.
    • (2010) Optim. Methods Softw. , vol.25 , pp. 895-916
    • Karmitsa, N.1    Makela, M.M.2
  • 26
    • 0000135467 scopus 로고
    • An exact penalty function algorithm for non-smooth convex constrained minimization problems
    • K. C. Kiwiel, An exact penalty function algorithm for non-smooth convex constrained minimization problems, IMA J. Numer. Anal., 5 (1985), pp. 111-119.
    • (1985) IMA J. Numer. Anal. , vol.5 , pp. 111-119
    • Kiwiel, K.C.1
  • 27
    • 0003296464 scopus 로고
    • Methods of descent for nondifferentiable optimization
    • Springer-Verlag, New York
    • K. C. Kiwiel, Methods of Descent for Nondifferentiable Optimization, Lecture Notes in Math. 1133, Springer-Verlag, New York, 1985.
    • (1985) Lecture Notes in Math. , vol.1133
    • Kiwiel, K.C.1
  • 28
    • 0000695140 scopus 로고
    • A constraint linearization method for nondifferentiable convex minimization
    • K. C. Kiwiel, A constraint linearization method for nondifferentiable convex minimization, Numer Math., 51 (1987), pp. 395-414.
    • (1987) Numer Math. , vol.51 , pp. 395-414
    • Kiwiel, K.C.1
  • 29
    • 34249923238 scopus 로고
    • Exact penalty functions in proximal bundle methods for constrained convex nondifferentiable minimization
    • K. C. Kiwiel, Exact penalty functions in proximal bundle methods for constrained convex nondifferentiable minimization, Math. Program., 52 (1991), pp. 285-302.
    • (1991) Math. Program. , vol.52 , pp. 285-302
    • Kiwiel, K.C.1
  • 30
    • 44649165114 scopus 로고    scopus 로고
    • Convergence of the gradient sampling algorithm for nonsmooth nonconvex optimization
    • K. C. Kiwiel, Convergence of the gradient sampling algorithm for nonsmooth nonconvex optimization, SIAM J. Optim., 18 (2007), pp. 379-388.
    • (2007) SIAM J. Optim. , vol.18 , pp. 379-388
    • Kiwiel, K.C.1
  • 31
    • 84884671380 scopus 로고    scopus 로고
    • Nonsmooth optimization via quasi-Newton methods
    • DOI 10.1007/s10107-012-0514-2
    • A. S. Lewis and M. L. Overton, Nonsmooth optimization via quasi-Newton methods, Math. Program., DOI 10.1007/s10107-012-0514-2.
    • Math. Program.
    • Lewis, A.S.1    Overton, M.L.2
  • 32
    • 0000009213 scopus 로고
    • An algorithm for constrained optimization with semismooth functions
    • R. Mifflin, An algorithm for constrained optimization with semismooth functions, Math.Oper. Res., 2 (1977), pp. 191-207.
    • (1977) Math.Oper. Res. , vol.2 , pp. 191-207
    • Mifflin, R.1
  • 33
    • 84966262179 scopus 로고
    • Updating quasi-Newton matrices with limited storage
    • J. Nocedal, Updating quasi-Newton matrices with limited storage, Math. Comput., 35 (1980), pp. 773-782.
    • (1980) Math. Comput. , vol.35 , pp. 773-782
    • Nocedal, J.1
  • 35
    • 0020718891 scopus 로고
    • On the extension of constrained optimization algorithms from differentiable to nondifferentiable problems
    • E. Polak, D. Q. Mayne, and Y. Wardi, On the extension of constrained optimization algorithms from differentiable to nondifferentiable problems, SIAM J. Control Optim., 21 (1983), pp. 179-203. (Pubitemid 13523238)
    • (1983) SIAM Journal on Control and Optimization , vol.21 , Issue.2 , pp. 179-203
    • Polak, E.1    Mayne, D.Q.2    Wardi, Y.3
  • 36
    • 0002207938 scopus 로고
    • A fast algorithm for nonlinearly constrained optimization calculations
    • Numerical Analysis, Springer, New York
    • M. J. D. Powell, A fast algorithm for nonlinearly constrained optimization calculations, in Numerical Analysis, Lecture Notes in Math. 630, Springer, New York, 1978, pp. 144-157.
    • (1978) Lecture Notes in Math. , vol.630 , pp. 144-157
    • Powell, M.J.D.1
  • 37
    • 0002741508 scopus 로고
    • Variable metric methods for constrained optimization
    • A. Bachem, M. Grötschel, and B. Korte, eds., Springer-Verlag, New York
    • M. J. D. Powell, Variable metric methods for constrained optimization, inMathematical Programming: The State of the Art, A. Bachem, M. Grötschel, and B. Korte, eds., Springer-Verlag, New York, 1983, pp. 288-311.
    • (1983) Mathematical Programming: The State of the Art , pp. 288-311
    • Powell, M.J.D.1
  • 39
    • 0002789370 scopus 로고
    • Lagrange multipliers and subderivatives of optimal value functions in nonlinear programming
    • R. T. Rockafellar, Lagrange multipliers and subderivatives of optimal value functions in nonlinear programming, in Math. Program. Study 17, 1982, pp. 28-66.
    • (1982) Math. Program. Study , vol.17 , pp. 28-66
    • Rockafellar, R.T.1
  • 40
    • 0021614264 scopus 로고
    • Exact penalty functions and stability in locally Lipschitz programming
    • E. Rosenberg, Exact penalty functions and stability in locally Lipschitz programming, Math. Program., 30 (1984), pp. 340-356. (Pubitemid 15454186)
    • (1984) Mathematical Programming , vol.30 , Issue.3 , pp. 340-356
    • Rosenberg, E.1
  • 41
  • 43
    • 0035537417 scopus 로고    scopus 로고
    • Data fitting problems with bounded uncertainties in the data
    • DOI 10.1137/S0895479899356596, PII S0895479899356596
    • G. A. Watson, Data fitting problems with bounded uncertainties in the data, SIAM J. Matrix Anal. Appl., 22 (2001), pp. 1274-1293. (Pubitemid 33401184)
    • (2001) SIAM Journal on Matrix Analysis and Applications , vol.22 , Issue.4 , pp. 1274-1293
    • Watson, G.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.