Local Convergence of an Inexact-Restoration Method and Numerical Experiments

Local convergence of an inexact-restoration method for nonlinear programming is proved. Numerical experiments are performed with the objective of evaluating the behavior of the purely local method against a globally convergent nonlinear programming algorithm.

[1]  J. B. Rosen.  The Gradient Projection Method for Nonlinear Programming. Part I. Linear Constraints , 1960 .

[2]  J. B. Rosen.  The gradient projection method for nonlinear programming: Part II , 1961 .

[3]  J. C. Heideman,et al.  Sequential gradient-restoration algorithm for the minimization of constrained functions—Ordinary and conjugate gradient versions , 1969 .

[4]  A. V. Levy,et al.  Modifications and extensions of the conjugate gradient-restoration algorithm for mathematical programming problems , 1971 .

[5]  R. Brent.  Some Efficient Algorithms for Solving Systems of Nonlinear Equations , 1973 .

[6]  José Mario Martínez,et al.  Generalization of the Methods of Brent and Brown for Solving Nonlinear Simultaneous Equations , 1979 .

[7]  Michel Cosnard,et al.  Numerical Solution of Nonlinear Equations , 1979, TOMS.

[8]  Michel Cosnard,et al.  Algorithm 554: BRENTM, A Fortran Subroutine for the Numerical Solution of Nonlinear Equations [C5] , 1980, TOMS.

[9]  José Mario Martínez,et al.  Solving nonlinear simultaneous equations with a generalization of Brent's method , 1980 .

[10]  Edward Michael Sims.  Sequential gradient-restoration algorithm for mathematical programming problems with inequality constraints , 1983 .

[11]  Arne Drud,et al.  CONOPT: A GRG code for large sparse dynamic nonlinear optimization problems , 1985, Math. Program..

[12]  P. Toint,et al.  A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds , 1991 .

[13]  L. Grippo,et al.  A class of nonmonotone stabilization methods in unconstrained optimization , 1991 .

[14]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[15]  Nicholas I. M. Gould,et al.  CUTE: constrained and unconstrained testing environment , 1995, TOMS.

[16]  Zdenek Dostál,et al.  Augmented Lagrangians with Adaptive Precision Control for Quadratic Programming with Equality Constraints , 1999, Comput. Optim. Appl..

[17]  José Mario Martínez,et al.  Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters , 1999, Math. Program..

[18]  J. M. Martínez,et al.  Inexact-Restoration Algorithm for Constrained Optimization1 , 2000 .

[19]  Z. Dostál,et al.  Solution of contact problems by FETI domain decomposition with natural coarse space projections , 2000 .

[20]  J. M. Martínez,et al.  Inexact-Restoration Method with Lagrangian Tangent Decrease and New Merit Function for Nonlinear Programming , 2001 .

[21]  José Mario Martínez,et al.  Large-Scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients , 2002, Comput. Optim. Appl..

[22]  Sven Leyffer,et al.  Nonlinear programming without a penalty function , 2002, Math. Program..

[23]  Zdenek Dostál,et al.  Augmented Lagrangians with Adaptive Precision Control for Quadratic Programming with Simple Bounds and Equality Constraints , 2002, SIAM J. Optim..

[24]  Clóvis C. Gonzaga,et al.  A Globally Convergent Filter Method for Nonlinear Programming , 2003, SIAM J. Optim..

[25]  José Mario Martínez,et al.  Inexact Restoration Methods for Nonlinear Programming: Advances and Perspectives , 2005 .