Abstract
This paper presents a successive quadratic programming algorithm for solving general nonlinear programming problems. In order to avoid the Maratos effect, direction-finding subproblems are derived by modifying the second-order approximations to both objective and constraint functions of the problem. We prove that the algorithm possesses global and superlinear convergence properties.
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M.C. Bartholomew-Biggs, “Recursive quadratic programming methods for nonlinear constraints“, in: M.J.D. Powell, ed.,Nonlinear Optimization 1981 (Academic Press, New York, 1982) pp. 213–221.
P.T. Boggs, J.W. Tolle and P. Wang, “On the local convergence of quasi-Newton methods for constrained optimization“,SIAM Journal on Control and Optimization 20 (1982) 161–171.
R.M. Chamberlain, M.J.D. Powell, C. Lemarechal and H.C. Pedersen, “The watchdog technique for forcing convergence in algorithms for constrained optimization“,Mathematical Programming Study 16 (1982) 1–17.
T.F. Coleman and A.R. Conn, “Nonlinear programming via an exact penalty function: Asymptotic analysis“,Mathematical Programming 24 (1982) 123–136.
T.F. Coleman and A.R. Conn, “Nonlinear programming via an exact penalty function: Global analysis“,Mathematical Programming 24 (1982) 137–161.
R. Fletcher,Practical methods of optimization, Vol. 2: Constrained optimization (John Wiley, Chichester, 1981).
R. Fletcher, “Second order corrections for nondifferentiable optimization“, in: G.A. Watson, ed.,Numerical analysis, Dundee 1981 (Springer-Verlag, Berlin, 1982) pp. 85–114.
D. Gabay, “Reduced quasi-Newton methods with feasibility improvement for nonlinearly constrained optimization“,Mathematical Programming Study 16 (1982) 18–44.
S.P. Han, “Superlinearly convergent variable metric algorithms for general nonlinear programming problems“,Mathematical Programming 11 (1976) 263–282.
S.P. Han, “A globally convergent method for nonlinear programming“,Journal of Optimization Theory and Applications 22 (1977) 297–309.
D.Q. Mayne and E. Polak, “A superlinearly convergent algorithm for constrained optimization problems“,Mathematical Programming Study 16 (1982) 45–61.
M.J.D. Powell, “A fast algorithm for nonlinearly constrained optimization calculations“, in: G.A. Watson, ed.,Numerical Analysis, Dundee 1977 (Springer-Verlag, Berlin, 1978) pp. 144–157.
M.J.D. Powell, “The convergence of variable metric methods for nonlinearly constrained optimization calculations“, in: O.L. Mangasarian, R.R. Meyer and S.M. Robinson, eds.,Nonlinear programming 3 (Academic Press, New York, 1978) 27–63.
M.J.D. Powell, “Variable metric methods for constrained optimization“, in: A. Bachem, M. Grötschel and B. Korte, eds.,Mathematical programming: The state of the art, Bonn 1982 (Springer-Verlag, Berlin, 1983) pp. 288–311.
K. Tone, “Revisions of constraint approximations in the successive QP method for nonlinear programming problems“,Mathematical Programming 26 (1983) 144–152.
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This work was supported in part by a Scientific Research Grant-in-Aid from the Ministry of Education, Science and Culture, Japan.
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Fukushima, M. A successive quadratic programming algorithm with global and superlinear convergence properties. Mathematical Programming 35, 253–264 (1986). https://doi.org/10.1007/BF01580879
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DOI: https://doi.org/10.1007/BF01580879