Sequential Quadratic Programming Methods for Nonlinear Programming

Sequential quadratic programming (SQP) methods are among the most effective techniques known today for solving nonlinearly constrained optimization problems. This paper presents an overview of SQP methods based on a quasi-Newton approximation to the Hessian of the Lagrangian function (or an augmented Lagrangian function). We briefly describe some of the issues in the formulation of SQP methods, including the form of the subproblem and the choice of merit function. We conclude with a list of available SQP software.

[1]  J. F. Price,et al.  An effective algorithm for minimization , 1967 .

[2]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[3]  P. Wolfe.  Convergence Conditions for Ascent Methods. II , 1969 .

[4]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[5]  B. V. Shah,et al.  Integer and Nonlinear Programming , 1971 .

[6]  F. A. Lootsma,et al.  Numerical methods for non-linear optimization , 1974 .

[7]  P. Gill,et al.  Quasi-Newton Methods for Unconstrained Optimization , 1972 .

[8]  Philip E. Gill,et al.  Numerical methods for constrained optimization , 1974 .

[9]  Stephen M. Robinson,et al.  Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear-programming algorithms , 1974, Math. Program..

[10]  J. J. Moré,et al.  Quasi-Newton Methods, Motivation and Theory , 1974 .

[11]  R. Rockafellar.  Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming , 1974 .

[12]  Shih-Ping Han.  Dual variable metric algorithms for constrained optimization , 1975, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[13]  Shih-Ping Han,et al.  Superlinearly convergent variable metric algorithms for general nonlinear programming problems , 1976, Math. Program..

[14]  M. H. Wright.  Numerical methods for nonlinearly constrained optimization , 1976 .

[15]  R. Tapia.  Diagonalized multiplier methods and quasi-Newton methods for constrained optimization , 1977 .

[16]  N. Maratos,et al.  Exact penalty function algorithms for finite dimensional and control optimization problems , 1978 .

[17]  M. J. D. Powell,et al.  A fast algorithm for nonlinearly constrained optimization calculations , 1978 .

[18]  L. Grippo,et al.  A New Class of Augmented Lagrangians in Nonlinear Programming , 1979 .

[19]  Olvi L. Mangasarian,et al.  Exact penalty functions in nonlinear programming , 1979, Math. Program..

[20]  T. M. Williams,et al.  Practical Methods of Optimization. Vol. 1: Unconstrained Optimization , 1980 .

[21]  P. Boggs,et al.  Augmented Lagrangians which are quadratic in the multiplier , 1980 .

[22]  R. Schnabel,et al.  A NEW DERIVATION OF SYMMETRIC POSITIVE DEFINITE SECANT UPDATES , 1980 .

[23]  R. Fletcher,et al.  Some numerical experience with a globally convergent algorithm for nonlinearly constrained optimization , 1980 .

[24]  Philip E. Gill,et al.  Practical optimization , 1981 .

[25]  K. Schittkowski.  On the Convergence of a Sequential Quadratic Programming Method with an Augmented Lagrangian Line Search Functions. , 1982 .

[26]  P. Boggs,et al.  On the Local Convergence of Quasi-Newton Methods for Constrained Optimization , 1982 .

[27]  Margaret H. Wright,et al.  Computation of the search direction in constrained optimization algorithms , 1982 .

[28]  D. Gabay.  Reduced quasi-Newton methods with feasibility improvement for nonlinearly constrained optimization , 1982 .

[29]  L. Grippo,et al.  A new augmented Lagrangian function for inequality constraints in nonlinear programming problems , 1982 .

[30]  Andrew R. Conn,et al.  Nonlinear programming via an exact penalty function: Asymptotic analysis , 1982, Math. Program..

[31]  D. Mayne,et al.  A surperlinearly convergent algorithm for constrained optimization problems , 1982 .

[32]  C. Lemaréchal,et al.  The watchdog technique for forcing convergence in algorithms for constrained optimization , 1982 .

[33]  Dimitri P. Bertsekas,et al.  Constrained Optimization and Lagrange Multiplier Methods , 1982 .

[34]  M. J. D. Powell,et al.  Variable Metric Methods for Constrained Optimization , 1982, ISMP.

[35]  K. Schittkowski.  The nonlinear programming method of Wilson, Han, and Powell with an augmented Lagrangian type line search function , 1982 .

[36]  M. J. D. Powell,et al.  VMCWD: a Fortran subroutine for constrained optimization , 1983, SMAP.

[37]  Martin Grötschel,et al.  Mathematical Programming The State of the Art, XIth International Symposium on Mathematical Programming, Bonn, Germany, August 23-27, 1982 , 1983, ISMP.

[38]  Kaoru Tone,et al.  Revisions of constraint approximations in the successive QP method for nonlinear programming problems , 1983, Math. Program..

[39]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[40]  P. Boggs,et al.  A family of descent functions for constrained optimization , 1984 .