메뉴 건너뛰기




Volumn 13, Issue 4, 2003, Pages 1098-1119

A sequential quadratically constrained quadratic programming method for differentiable convex minimization

Author keywords

Convex programming; Global convergence; Maratos effect; Quadratic convergence; Quadratically constrained quadratic programming

Indexed keywords


EID: 0242595924     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623401398120     Document Type: Article
Times cited : (49)

References (27)
  • 1
    • 0009969106 scopus 로고    scopus 로고
    • Symmetric cones, potential reduction methods
    • H. Wolkowicz, R. Saigal, and L. Vandenberghe, eds., Kluwer Academic Publishers, Boston, MA
    • F. ALIZADEH AND S. SCHMIETA, Symmetric cones, potential reduction methods, in Handbook of Semidefinite Programming, H. Wolkowicz, R. Saigal, and L. Vandenberghe, eds., Kluwer Academic Publishers, Boston, MA, 2000, pp. 195-233.
    • (2000) Handbook of Semidefinite Programming , pp. 195-233
    • Alizadeh, F.1    Schmieta, S.2
  • 2
    • 0036433570 scopus 로고    scopus 로고
    • A superlinearly convergent sequential quadratically constrained quadratic programming algorithm for degenerate nonlinear programming
    • M. ANITESCU, A superlinearly convergent sequential quadratically constrained quadratic programming algorithm for degenerate nonlinear programming, SIAM J. Optim., 12 (2002), pp. 949-978.
    • (2002) SIAM J. Optim. , vol.12 , pp. 949-978
    • Anitescu, M.1
  • 4
    • 44649149897 scopus 로고
    • Sequential Quadratic Programming
    • Cambridge University Press, Cambridge, UK
    • B.T. BOGGS AND J.W. TOLLE, Sequential Quadratic Programming, Acta Numer. 4, Cambridge University Press, Cambridge, UK, 1995, pp. 1-51.
    • (1995) Acta Numer. 4 , pp. 1-51
    • Boggs, B.T.1    Tolle, J.W.2
  • 5
    • 34250234852 scopus 로고
    • Nonlinear programming via an exact penalty function: Global analysis
    • T.F. COLEMAN AND A.R. CONN, Nonlinear programming via an exact penalty function: Global analysis, Math. Programming, 24 (1982), pp. 137-161.
    • (1982) Math. Programming , vol.24 , pp. 137-161
    • Coleman, T.F.1    Conn, A.R.2
  • 6
    • 0030541525 scopus 로고    scopus 로고
    • On the formulation and theory of the Newton interior-point method for nonlinear programming
    • A.S. EL-BAKRY, R.A. TAPIA, T. TSUCHIYA, AND Y. ZHANG, On the formulation and theory of the Newton interior-point method for nonlinear programming, J. Optim. Theory Appl., 89 (1996), pp. 507-541.
    • (1996) J. Optim. Theory Appl. , vol.89 , pp. 507-541
    • El-Bakry, A.S.1    Tapia, R.A.2    Tsuchiya, T.3    Zhang, Y.4
  • 7
    • 0020199513 scopus 로고
    • A finitely convergent algorithm for convex inequalities
    • M. FUKUSHIMA, A finitely convergent algorithm for convex inequalities, IEEE Trans. Autom. Contr., 27 (1982), pp. 1126-1127.
    • (1982) IEEE Trans. Autom. Contr. , vol.27 , pp. 1126-1127
    • Fukushima, M.1
  • 8
    • 0022751474 scopus 로고
    • A successive quadratic programming algorithm with global and superlinear convergence properties
    • M. FUKUSHIMA, A successive quadratic programming algorithm with global and superlinear convergence properties, Math. Programming, 35 (1986), pp. 253-264.
    • (1986) Math. Programming , vol.35 , pp. 253-264
    • Fukushima, M.1
  • 9
    • 0000699491 scopus 로고
    • On approximate solutions of systems of linear inequalities
    • A.J. HOFFMAN, On approximate solutions of systems of linear inequalities, J. Research Nat. Bur. Standards, 49 (1952), pp. 263-265.
    • (1952) J. Research Nat. Bur. Standards , vol.49 , pp. 263-265
    • Hoffman, A.J.1
  • 10
    • 0007232735 scopus 로고    scopus 로고
    • SQ2P, sequential quadratic constrained quadratic programming
    • Y.X. Yuan, ed., Kluwer Academic Publishers, Dordrecht, The Netherlands
    • S. KRUK AND H. WOLKOWICZ, SQ2P, sequential quadratic constrained quadratic programming, in Advances in Nonlinear Programming, Y.X. Yuan, ed., Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998, pp. 177-204.
    • (1998) Advances in Nonlinear Programming , pp. 177-204
    • Kruk, S.1    Wolkowicz, H.2
  • 11
    • 0011630075 scopus 로고    scopus 로고
    • Sequential, quadratic constrained, quadratic programming for general nonlinear programming
    • H. Wolkowicz, R. Saigal, and L. Vandenberghe, eds., Kluwer Academic Publishers, Boston, MA
    • S. KRUK AND H. WOLKOWICZ, Sequential, quadratic constrained, quadratic programming for general nonlinear programming, in Handbook of Semidefinite Programming, H. Wolkowicz, R. Saigal, and L. Vandenberghe, eds., Kluwer Academic Publishers, Boston, MA, 2000, pp. 563-575.
    • (2000) Handbook of Semidefinite Programming , pp. 563-575
    • Kruk, S.1    Wolkowicz, H.2
  • 13
    • 0008971685 scopus 로고    scopus 로고
    • On extensions of Frank-Wolfe Theorems
    • Z.-Q. LUO AND S. ZHANG, On extensions of Frank-Wolfe Theorems, Comput. Optim. Appl., 13 (1999), pp. 87-110.
    • (1999) Comput. Optim. Appl. , vol.13 , pp. 87-110
    • Luo, Z.-Q.1    Zhang, S.2
  • 14
    • 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. Programming Stud., 16 (1982), pp. 45-61.
    • (1982) Math. Programming Stud. , vol.16 , pp. 45-61
    • Mayne, D.Q.1    Polak, E.2
  • 15
    • 0001856065 scopus 로고    scopus 로고
    • Polynomial convergence of primal-dual algorithms for the second-order cone programs based on the MZ-family of directions
    • R.D.C. MONTEIRO AND T. TSUCHIYA, Polynomial convergence of primal-dual algorithms for the second-order cone programs based on the MZ-family of directions, Math. Program., 88 (2000), pp. 61-83.
    • (2000) Math. Program. , vol.88 , pp. 61-83
    • Monteiro, R.D.C.1    Tsuchiya, T.2
  • 16
    • 0003254248 scopus 로고
    • Interior-point Polynomial Algorithms in Convex Programming
    • Siam, Philadelphia, Pa
    • Y. NESTEROV AND A. NEMIROVSKII, Interior-Point Polynomial Algorithms in Convex Programming, SIAM Stud. Appl. Math. 13, SIAM, Philadelphia, PA, 1994.
    • (1994) Siam Stud. Appl. Math. , vol.13
    • Nesterov, Y.1    Nemirovskii, A.2
  • 17
    • 0010746895 scopus 로고    scopus 로고
    • Infeasible-start primal-dual methods and infeasibility detectors for nonlinear programming problems
    • Y.E. NESTEROV, M.J. TODD, AND Y. YE, Infeasible-start primal-dual methods and infeasibility detectors for nonlinear programming problems, Math. Program., 84 (1999), pp. 227-267.
    • (1999) Math. Program. , vol.84 , pp. 227-267
    • Nesterov, Y.E.1    Todd, M.J.2    Ye, Y.3
  • 19
    • 0242502860 scopus 로고
    • A second-order method for the discrete min-max problem
    • V.M. PANIN, A second-order method for the discrete min-max problem, U.S.S.R. Comput. Math. and Math. Phys., 19 (1) (1979), pp. 90-100.
    • (1979) U.S.S.R. Comput. Math. and Math. Phys. , vol.19 , Issue.1 , pp. 90-100
    • Panin, V.M.1
  • 20
    • 0242587507 scopus 로고
    • Some methods of solving convex programming problems
    • V.M. PANIN, Some methods of solving convex programming problems, U.S.S.R. Comput. Math. and Math. Phys., 21 (2) (1981), pp. 57-72.
    • (1981) U.S.S.R. Comput. Math. and Math. Phys. , vol.21 , Issue.2 , pp. 57-72
    • Panin, V.M.1
  • 21
    • 0026836629 scopus 로고
    • On the extension of Newton's method to semi-infinite minimax problems
    • E. POLAK, D.Q. MAYNE, AND J.E. HIGGINS, On the extension of Newton's method to semi-infinite minimax problems, SIAM J. Control Optim., 30 (1992), pp. 367-389.
    • (1992) SIAM J. Control Optim. , vol.30 , pp. 367-389
    • Polak, E.1    Mayne, D.Q.2    Higgins, J.E.3
  • 22
    • 0002741508 scopus 로고
    • Variable metric methods for constrained optimization
    • A. Bachem, M. Grötschel, and B. Korte, eds., Springer-Verlag, Berlin
    • M.J.D. POWELL, Variable metric methods for constrained optimization, in Mathematical Programming: State of the Art, A. Bachem, M. Grötschel, and B. Korte, eds., Springer-Verlag, Berlin, 1983, pp. 288-311.
    • (1983) Mathematical Programming: State of the Art , pp. 288-311
    • Powell, M.J.D.1
  • 23
    • 0002893535 scopus 로고    scopus 로고
    • Superlinear convergence of an interior-point method for monotone variational inequalities
    • M.C. Ferris and J.-S. Pang, eds., SIAM, Philadelphia
    • D. RALPH AND S.J. WRIGHT, Superlinear convergence of an interior-point method for monotone variational inequalities, in Complementarity and Variational Problems: State of the Art, M.C. Ferris and J.-S. Pang, eds., SIAM, Philadelphia, 1997, pp. 345-385.
    • (1997) Complementarity and Variational Problems: State of the Art , pp. 345-385
    • Ralph, D.1    Wright, S.J.2
  • 24
    • 0029195774 scopus 로고
    • Linear programming, complexity theory and elementary functional analysis
    • J. RENEGAR, Linear programming, complexity theory and elementary functional analysis, Math. Programming, 70 (1995), pp. 279-351.
    • (1995) Math. Programming , vol.70 , pp. 279-351
    • Renegar, J.1
  • 25
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, NJ
    • R.T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 26
    • 0033293480 scopus 로고    scopus 로고
    • A convergence analysis of the scaling-invariant primal-dual path-following algorithms for second-order cone programming
    • T. TSUCHIYA, A convergence analysis of the scaling-invariant primal-dual path-following algorithms for second-order cone programming, Optim. Methods Softw., 11/12 (1999), pp. 141-182.
    • (1999) Optim. Methods Softw. , vol.11-12 , pp. 141-182
    • Tsuchiya, T.1
  • 27
    • 0004594843 scopus 로고
    • A generalized quadratic programming-based phase-I-phase-II method for inequality-constrained optimization
    • E.J. WIEST AND E. POLAK, A generalized quadratic programming-based phase-I-phase-II method for inequality-constrained optimization, Appl. Math. Optim., 26 (1992), pp. 223-252.
    • (1992) Appl. Math. Optim. , vol.26 , pp. 223-252
    • Wiest, E.J.1    Polak, E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.