A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints

An algorithm is described for solving large-scale nonlinear programs whose objective and constraint functions are smooth and continuously differentiable. The algorithm is of the projected Lagrangian type, involving a sequence of sparse, linearly constrained subproblems whose objective functions include a modified Lagrangian term and a modified quadratic penalty function.

[1]  R. E. Griffith,et al.  A Nonlinear Programming Technique for the Optimization of Continuous Processing Systems , 1961 .

[2]  J. F. Benders.  Partitioning procedures for solving mixed-variables programming problems , 1962 .

[3]  B. V. Dean,et al.  Studies in Linear and Non-Linear Programming. , 1959 .

[4]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

[5]  J. B. Rosen.  Iterative Solution of Nonlinear Optimal Control Problems , 1966 .

[6]  Garth P. McCormick,et al.  A Nonlinear Programming Model for Launch Vehicle Design and Costing , 1967, Oper. Res..

[7]  M. Hestenes.  Multiplier and gradient methods , 1969 .

[8]  C. M. Shen,et al.  Determination of optimum power-system operating conditions under constraints , 1969 .

[9]  Leon S. Lasdon,et al.  Optimization Theory of Large Systems , 1970 .

[10]  R. Meyer.  The Validity of a Family of Optimization Methods , 1970 .

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

[12]  Eli Hellerman,et al.  The Partitioned Preassigned Pivot Procedure (P4) , 1972 .

[13]  R. Willoughby.  Sparse matrices and their applications , 1972 .

[14]  S. M. Robinson,et al.  A quadratically-convergent algorithm for general nonlinear programming problems , 1972, Math. Program..

[15]  B. A. Murtagh,et al.  Projection methods for non-linear programming , 1973, Math. Program..

[16]  P. Ritch.  Discrete optimal control with multiple constraints I Constraint separation and transformation technique , 1973 .

[17]  Philip E. Gill,et al.  Newton-type methods for unconstrained and linearly constrained optimization , 1974, Math. Program..

[18]  Michael A. Saunders,et al.  A FAST, STABLE IMPLEMENTATION OF THE SIMPLEX METHOD USING BARTELS-GOLUB UPDATING , 1976 .

[19]  Olvi L. Mangasarian,et al.  Superlinearly convergent quasi-newton algorithms for nonlinearly constrained optimization problems , 1976, Math. Program..

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

[21]  Ron S. Dembo,et al.  A set of geometric programming test problems and their solutions , 1976, Math. Program..

[22]  M. A. Laughton,et al.  Optimal electric power scheduling: A large nonlinear programming test problem solved by recursive quadratic programming , 1977, Math. Program..

[23]  Harvey J. Greenberg,et al.  Design and implementation of optimization software , 1977, Math. Program..

[24]  Michael A Saunders,et al.  MINOS System Manual. , 1977 .

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

[26]  E. M. L. Beale.  Nonlinear Programming Using a General Mathematical Programming System , 1978 .

[27]  Leon S. Lasdon,et al.  Generalized Reduced Gradient Software for Linearly and Nonlinearly Constrained Problems , 1978 .

[28]  J. B. Rosen.  TWO-PHASE ALGORITHM FOR NONLINEAR CONSTRAINT PROBLEMS11This research was supported in part by the National Science Foundation grant MCS 76-23311. Support by the Systems Optimization Lab, Department of Operations Research, Stanford University, during the author's sabbatical leave, is also gratefully , 1978 .

[29]  M. J. D. Powell,et al.  Algorithms for nonlinear constraints that use lagrangian functions , 1978, Math. Program..

[30]  Michael A. Saunders,et al.  Large-scale linearly constrained optimization , 1978, Math. Program..

[31]  S. E. Jacobsen,et al.  Reverse convex programming , 1980 .

[32]  Paul Preckel,et al.  Modules for Use with MINOS/AUGMENTED in Solving Sequences of Mathematical Programming. , 1980 .

[33]  Michael A. Saunders,et al.  MINOS/AUGMENTED User's Manual. , 1980 .

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

[35]  Lamberto Cesari,et al.  Optimization-Theory And Applications , 1983 .