An inexact Newton method combined with Hestenes multipliers’ scheme for the solution of Karush–Kuhn–Tucker systems
In this work a Newton interior-point method for the solution of Karush–Kuhn–Tucker systems is presented. A crucial feature of this iterative method is the solution, at each iteration, of the inner subproblem. This subproblem is a linear-quadratic programming problem, that can solved approximately by...
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| Published in: | Applied mathematics and computation Vol. 168; no. 1; pp. 651 - 676 |
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| Abstract | In this work a Newton interior-point method for the solution of Karush–Kuhn–Tucker systems is presented.
A crucial feature of this iterative method is the solution, at each iteration, of the inner subproblem. This subproblem is a linear-quadratic programming problem, that can solved approximately by an inner iterative method such as the Hestenes multipliers’ method.
A deep analysis on the choices of the parameters of the method (perturbation and damping parameters) has been done.
The global convergence of the Newton interior-point method is proved when it is viewed as an inexact Newton method for the solution of nonlinear systems with restriction on the sign of some variables.
The Newton interior-point method is numerically evaluated on large scale test problems arising from elliptic optimal control problems which show the effectiveness of the approach. |
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| AbstractList | In this work a Newton interior-point method for the solution of Karush–Kuhn–Tucker systems is presented.
A crucial feature of this iterative method is the solution, at each iteration, of the inner subproblem. This subproblem is a linear-quadratic programming problem, that can solved approximately by an inner iterative method such as the Hestenes multipliers’ method.
A deep analysis on the choices of the parameters of the method (perturbation and damping parameters) has been done.
The global convergence of the Newton interior-point method is proved when it is viewed as an inexact Newton method for the solution of nonlinear systems with restriction on the sign of some variables.
The Newton interior-point method is numerically evaluated on large scale test problems arising from elliptic optimal control problems which show the effectiveness of the approach. |
| Author | Galligani, Emanuele Ruggiero, Valeria Bonettini, Silvia |
| Author_xml | – sequence: 1 givenname: Silvia surname: Bonettini fullname: Bonettini, Silvia email: bonettini.silvia@unimo.it organization: Dipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi 213/b, 41100 Modena, Italy – sequence: 2 givenname: Emanuele surname: Galligani fullname: Galligani, Emanuele email: galligan@unimo.it organization: Dipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi 213/b, 41100 Modena, Italy – sequence: 3 givenname: Valeria surname: Ruggiero fullname: Ruggiero, Valeria email: rgv@dns.unife.it organization: Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, 44100 Ferrara, Italy |
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| Keywords | Elliptic control problems Newton interior-point method Inexact Newton method Large scale nonlinear programming problems Hestenes multipliers’ method Damping Hestenes method Interior point method Iterative method Linear programming Non linear programming Quadratic programming Non linear system Convergence Perturbation method Numerical analysis Applied mathematics Perturbation techniques Hestenes multipliers' method Multiplier Large scale Newton method |
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| References | Durazzi, Ruggiero, Zanghirati (bib8) 2001; 110 Nocedal, Wright (bib19) 1999 Durazzi, Galligani (bib5) 2001; vol. 58 Saad (bib21) 1996 I.S. Duff, J.K. Reid, MA27-a set of Fortran subroutines for solving sparse symmetric sets of linear equations, Tech Report AERE R10533, HMSO, London, 1982. Rheinboldt (bib20) 1998 El-Bakry, Tapia, Tsuchiya, Zhang (bib10) 1996; 89 Eisenstat, Walker (bib9) 1994; 4 Hestenes (bib13) 1975 Durazzi (bib4) 2000; 104 Liu, Ng, Peyton (bib14) 1993; 14 Vanderbei, Shanno (bib22) 1999; 13 Mittelmann, Maurer (bib18) 2000; 120 E. Galligani, Analysis of the convergence of an inexact Newton method for solving Karush–Kuhn–Tucker systems, Atti Sem. Matem. Fis. Univ. Modena, in press. Maurer, Mittelmann (bib16) 2000; 16 Dennis, Schnabel (bib2) 1983 Durazzi, Ruggiero (bib6) 2004; 120 Dembo, Eisenstat, Steihaug (bib1) 1982; 19 Luenberger (bib15) 1984 Maurer, Mittelmann (bib17) 2001; 18 C. Durazzi, V. Ruggiero, A Newton inexact interior-point method for large scale nonlinear optimization problems, Annali Univ. Ferrara, Sez. VII, Sc. Matem. IL, (2003) 333–357. Gould (bib12) 1985; 32 Maurer (10.1016/j.amc.2004.09.018_bib17) 2001; 18 Luenberger (10.1016/j.amc.2004.09.018_bib15) 1984 Rheinboldt (10.1016/j.amc.2004.09.018_bib20) 1998 Dembo (10.1016/j.amc.2004.09.018_bib1) 1982; 19 10.1016/j.amc.2004.09.018_bib7 Eisenstat (10.1016/j.amc.2004.09.018_bib9) 1994; 4 Durazzi (10.1016/j.amc.2004.09.018_bib8) 2001; 110 Durazzi (10.1016/j.amc.2004.09.018_bib5) 2001; vol. 58 10.1016/j.amc.2004.09.018_bib11 10.1016/j.amc.2004.09.018_bib3 El-Bakry (10.1016/j.amc.2004.09.018_bib10) 1996; 89 Dennis (10.1016/j.amc.2004.09.018_bib2) 1983 Durazzi (10.1016/j.amc.2004.09.018_bib6) 2004; 120 Saad (10.1016/j.amc.2004.09.018_bib21) 1996 Durazzi (10.1016/j.amc.2004.09.018_bib4) 2000; 104 Mittelmann (10.1016/j.amc.2004.09.018_bib18) 2000; 120 Maurer (10.1016/j.amc.2004.09.018_bib16) 2000; 16 Hestenes (10.1016/j.amc.2004.09.018_bib13) 1975 Nocedal (10.1016/j.amc.2004.09.018_bib19) 1999 Liu (10.1016/j.amc.2004.09.018_bib14) 1993; 14 Gould (10.1016/j.amc.2004.09.018_bib12) 1985; 32 Vanderbei (10.1016/j.amc.2004.09.018_bib22) 1999; 13 |
| References_xml | – volume: 89 start-page: 507 year: 1996 end-page: 541 ident: bib10 article-title: On the formulation and theory of Newton interior-point method for nonlinear programming publication-title: J. Optim. Theory Appl. – year: 1984 ident: bib15 article-title: Linear and Nonlinear Programming – volume: 120 start-page: 175 year: 2000 end-page: 195 ident: bib18 article-title: Solving elliptic control problems with interior point and SQP methods: control and state constraint publication-title: J. Comput. Appl. Math. – volume: 120 start-page: 199 year: 2004 end-page: 208 ident: bib6 article-title: Global convergence of the Newton interior-point method for nonlinear programming publication-title: J. Optim. Theory Appl. – year: 1999 ident: bib19 article-title: Numerical Optimization – volume: 4 start-page: 393 year: 1994 end-page: 422 ident: bib9 article-title: Globally convergent inexact Newton methods publication-title: SIAM J. Optim. – reference: E. Galligani, Analysis of the convergence of an inexact Newton method for solving Karush–Kuhn–Tucker systems, Atti Sem. Matem. Fis. Univ. Modena, in press. – year: 1998 ident: bib20 article-title: Methods for Solving Systems of Nonlinear Equations – volume: 13 start-page: 231 year: 1999 end-page: 252 ident: bib22 article-title: An interior-point algorithm for nonconvex nonlinear programming publication-title: Comput. Optim. Appl. – reference: I.S. Duff, J.K. Reid, MA27-a set of Fortran subroutines for solving sparse symmetric sets of linear equations, Tech Report AERE R10533, HMSO, London, 1982. – reference: C. Durazzi, V. Ruggiero, A Newton inexact interior-point method for large scale nonlinear optimization problems, Annali Univ. Ferrara, Sez. VII, Sc. Matem. IL, (2003) 333–357. – volume: 18 start-page: 141 year: 2001 end-page: 160 ident: bib17 article-title: Optimization techniques for solving elliptic control problems with control and state constraints: Part 2. Distributed control publication-title: Comput. Optim. Appl. – year: 1996 ident: bib21 article-title: Iterative Methods for Sparse Linear System – volume: 32 start-page: 90 year: 1985 end-page: 99 ident: bib12 article-title: On practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem publication-title: Math. Program. – year: 1975 ident: bib13 article-title: Optimization Theory. The Finite Dimensional Case – volume: 19 start-page: 400 year: 1982 end-page: 408 ident: bib1 article-title: Inexact Newton methods publication-title: SIAM J. Numer. Anal. – year: 1983 ident: bib2 article-title: Numerical Methods for Unconstrained Optimization and Nonlinear Equations – volume: 104 start-page: 73 year: 2000 end-page: 90 ident: bib4 article-title: On the Newton interior-point method for nonlinear programming problems publication-title: J. Optim. Theory Appl. – volume: 110 start-page: 289 year: 2001 end-page: 313 ident: bib8 article-title: Parallel interior-point method for linear and quadratic programs with special structure publication-title: J. Optim. Theory Appl. – volume: 16 start-page: 29 year: 2000 end-page: 55 ident: bib16 article-title: Optimization techniques for solving elliptic control problems with control and state constraints: Part 1. Boundary control publication-title: Comput. Optim. Appl. – volume: vol. 58 start-page: 71 year: 2001 end-page: 99 ident: bib5 article-title: Nonlinear programming methods for solving optimal control problems publication-title: Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models Nonconvex Optimization and Its Applications – volume: 14 start-page: 242 year: 1993 end-page: 252 ident: bib14 article-title: On finding supernodes for sparse matrix computations publication-title: SIAM J. Matrix Anal. Appl. – volume: 110 start-page: 289 year: 2001 ident: 10.1016/j.amc.2004.09.018_bib8 article-title: Parallel interior-point method for linear and quadratic programs with special structure publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1017523228692 – year: 1984 ident: 10.1016/j.amc.2004.09.018_bib15 – ident: 10.1016/j.amc.2004.09.018_bib11 – volume: 120 start-page: 199 year: 2004 ident: 10.1016/j.amc.2004.09.018_bib6 article-title: Global convergence of the Newton interior-point method for nonlinear programming publication-title: J. Optim. Theory Appl. doi: 10.1023/B:JOTA.0000012969.51013.2c – volume: 104 start-page: 73 year: 2000 ident: 10.1016/j.amc.2004.09.018_bib4 article-title: On the Newton interior-point method for nonlinear programming problems publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1004624721836 – volume: 4 start-page: 393 year: 1994 ident: 10.1016/j.amc.2004.09.018_bib9 article-title: Globally convergent inexact Newton methods publication-title: SIAM J. Optim. doi: 10.1137/0804022 – volume: 89 start-page: 507 year: 1996 ident: 10.1016/j.amc.2004.09.018_bib10 article-title: On the formulation and theory of Newton interior-point method for nonlinear programming publication-title: J. Optim. Theory Appl. doi: 10.1007/BF02275347 – volume: 14 start-page: 242 year: 1993 ident: 10.1016/j.amc.2004.09.018_bib14 article-title: On finding supernodes for sparse matrix computations publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/0614019 – year: 1998 ident: 10.1016/j.amc.2004.09.018_bib20 – volume: 19 start-page: 400 year: 1982 ident: 10.1016/j.amc.2004.09.018_bib1 article-title: Inexact Newton methods publication-title: SIAM J. Numer. Anal. doi: 10.1137/0719025 – ident: 10.1016/j.amc.2004.09.018_bib3 – year: 1999 ident: 10.1016/j.amc.2004.09.018_bib19 – volume: 120 start-page: 175 year: 2000 ident: 10.1016/j.amc.2004.09.018_bib18 article-title: Solving elliptic control problems with interior point and SQP methods: control and state constraint publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(00)00309-5 – volume: 16 start-page: 29 year: 2000 ident: 10.1016/j.amc.2004.09.018_bib16 article-title: Optimization techniques for solving elliptic control problems with control and state constraints: Part 1. Boundary control publication-title: Comput. Optim. Appl. doi: 10.1023/A:1008725519350 – ident: 10.1016/j.amc.2004.09.018_bib7 doi: 10.1007/BF02844922 – volume: 13 start-page: 231 year: 1999 ident: 10.1016/j.amc.2004.09.018_bib22 article-title: An interior-point algorithm for nonconvex nonlinear programming publication-title: Comput. Optim. Appl. doi: 10.1023/A:1008677427361 – year: 1996 ident: 10.1016/j.amc.2004.09.018_bib21 – volume: vol. 58 start-page: 71 year: 2001 ident: 10.1016/j.amc.2004.09.018_bib5 article-title: Nonlinear programming methods for solving optimal control problems – year: 1975 ident: 10.1016/j.amc.2004.09.018_bib13 – year: 1983 ident: 10.1016/j.amc.2004.09.018_bib2 – volume: 18 start-page: 141 year: 2001 ident: 10.1016/j.amc.2004.09.018_bib17 article-title: Optimization techniques for solving elliptic control problems with control and state constraints: Part 2. Distributed control publication-title: Comput. Optim. Appl. doi: 10.1023/A:1008774521095 – volume: 32 start-page: 90 year: 1985 ident: 10.1016/j.amc.2004.09.018_bib12 article-title: On practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem publication-title: Math. Program. doi: 10.1007/BF01585660 |
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| Snippet | In this work a Newton interior-point method for the solution of Karush–Kuhn–Tucker systems is presented.
A crucial feature of this iterative method is the... |
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| SubjectTerms | Calculus of variations and optimal control Elliptic control problems Exact sciences and technology Global analysis, analysis on manifolds Hestenes multipliers’ method Inexact Newton method Large scale nonlinear programming problems Mathematical analysis Mathematics Newton interior-point method Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| Title | An inexact Newton method combined with Hestenes multipliers’ scheme for the solution of Karush–Kuhn–Tucker systems |
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