Large-scale linearly constrained optimization

An algorithm for solving large-scale nonlinear programs with linear constraints is presented. The method combines efficient sparse-matrix techniques as in the revised simplex method with stable quasi-Newton methods for handling the nonlinearities. A general-purpose production code (MINOS) is described, along with computational experience on a wide variety of problems.

[1]  P. Wolfe.  THE SIMPLEX METHOD FOR QUADRATIC PROGRAMMING , 1959 .

[2]  Roger Fletcher,et al.  A Rapidly Convergent Descent Method for Minimization , 1963, Comput. J..

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

[4]  C. M. Reeves,et al.  Function minimization by conjugate gradients , 1964, Comput. J..

[5]  C. E. Lemke,et al.  Bimatrix Equilibrium Points and Mathematical Programming , 1965 .

[6]  G. McCormick,et al.  Selected applications of nonlinear programming , 1968 .

[7]  D. Goldfarb.  Extension of Davidon’s Variable Metric Method to Maximization Under Linear Inequality and Equality Constraints , 1969 .

[8]  Gene H. Golub,et al.  The simplex method of linear programming using LU decomposition , 1969, Commun. ACM.

[9]  G. McCormick.  A Second Order Method for the Linearly Constrained Nonlinear Programming Problem , 1970 .

[10]  G. McCormick.  The Variable Reduction Method for Nonlinear Programming , 1970 .

[11]  Eli Hellerman,et al.  Reinversion with the preassigned pivot procedure , 1971, Math. Program..

[12]  R. Bartels.  A stabilization of the simplex method , 1971 .

[13]  James E. Kalan.  Aspects of large-scale in-core linear programming , 1971, ACM '71.

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

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

[16]  David Mautner Himmelblau,et al.  Applied Nonlinear Programming , 1972 .

[17]  M. Saunders.  Large-scale linear programming using the Cholesky factorization , 1972 .

[18]  E. Polak,et al.  Computational methods in optimization : a unified approach , 1972 .

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

[20]  Richard P. Brent,et al.  Reducing the retrieval time of scatter storage techniques , 1973, Commun. ACM.

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

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

[23]  A. Manne.  Waiting for the breeder , 1974 .

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

[25]  John A. Tomlin,et al.  On pricing and backward transformation in linear programming , 1974, Math. Program..

[26]  Åke Björck,et al.  Numerical Methods , 2021, Markov Renewal and Piecewise Deterministic Processes.

[27]  P. Gill,et al.  Methods for computing and modifying the $LDV$ factors of a matrix , 1975 .

[28]  B. Murtagh,et al.  The modelling of energy production and consumption in New Zealand , 1975 .

[29]  A. Buckley,et al.  An alternate implementation of Goldfarb's minimization algorithm , 1975, Math. Program..

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

[31]  A. Manne.  U.S. options for a transition from oil and gas to synthetic fuels , 1976 .

[32]  A. Conn.  Linear Programming via a Nondifferentiable Penalty Function , 1976 .

[33]  A. Manne.  ETA: A MODEL FOR ENERGY TECHNOLOGY ASSESSMENT , 1976 .

[34]  M. J. D. Powell,et al.  Restart procedures for the conjugate gradient method , 1977, Math. Program..

[35]  Donald Goldfarb,et al.  On the Bartels—Golub decomposition for linear programming bases , 1977, Math. Program..

[36]  John K. Reid,et al.  An Implementation of Tarjan's Algorithm for the Block Triangularization of a Matrix , 1978, TOMS.

[37]  J. Tomlin.  Robust implementation of Lemke's method for the linear complementarity problem , 1978 .