×

An exact penalty-Lagrangian approach for large-scale nonlinear programming. (English) Zbl 1279.90161

Summary: Nonlinear programming problems with equality constraints and bound constraints on the variables are considered. The presence of bound constraints in the definition of the problem is exploited as much as possible. To this aim, an efficient search direction is defined which is able to produce a locally and superlinearly convergent algorithm and that can be computed in an efficient way by using a truncated scheme suitable for large scale problems. Then, an exact merit function is considered whose analytical expression again exploits the particular structure of the problem by using an exact augmented Lagrangian approach for equality constraints and an exact penalty approach for the bound constraints. It is proved that the search direction and the merit function have some strong connections which can be the basis to define a globally convergent algorithm with superlinear convergence rate for the solution of the constrained problem.

MSC:

90C30 Nonlinear programming
90C06 Large-scale problems in mathematical programming

Software:

TANGO; Ipopt
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1137/060654797 · Zbl 1151.49027 · doi:10.1137/060654797
[2] DOI: 10.1093/imamat/21.1.67 · Zbl 0373.90056 · doi:10.1093/imamat/21.1.67
[3] Bartholomew-Biggs MC, Math. Program. Study 31 pp 21– (1987)
[4] DOI: 10.1023/A:1020533003783 · Zbl 1022.90017 · doi:10.1023/A:1020533003783
[5] Bertsekas DP, Constrained Optimization and Lagrange Multiplier Methods (1982)
[6] Bertsekas DP, Nonlinear Programming (1999)
[7] DOI: 10.1080/10556780701577730 · Zbl 1211.90222 · doi:10.1080/10556780701577730
[8] Byrd RH, Math. Program. Ser. B 100 pp 27– (2004)
[9] DOI: 10.1137/S1052623497325107 · Zbl 0957.65057 · doi:10.1137/S1052623497325107
[10] DOI: 10.1080/10556780701394169 · Zbl 1211.90224 · doi:10.1080/10556780701394169
[11] DOI: 10.1007/s10107-003-0378-6 · Zbl 1023.90060 · doi:10.1007/s10107-003-0378-6
[12] DOI: 10.1090/S0025-5718-97-00777-1 · Zbl 0854.90125 · doi:10.1090/S0025-5718-97-00777-1
[13] DOI: 10.1007/s10589-008-9216-3 · Zbl 1209.90317 · doi:10.1007/s10589-008-9216-3
[14] DOI: 10.1080/02331939308843909 · Zbl 0818.90104 · doi:10.1080/02331939308843909
[15] DOI: 10.1023/A:1008675917367 · Zbl 1040.90565 · doi:10.1023/A:1008675917367
[16] DOI: 10.1080/10556780008805793 · Zbl 0988.90037 · doi:10.1080/10556780008805793
[17] DOI: 10.1023/A:1022901020289 · Zbl 1038.90099 · doi:10.1023/A:1022901020289
[18] DOI: 10.1007/BF02192227 · Zbl 0830.90125 · doi:10.1007/BF02192227
[19] Fiacco AV, Nonlinear Programming: Sequential Unconstrained Optimization Techniques (1986)
[20] DOI: 10.1137/S1052623499357258 · Zbl 1038.90076 · doi:10.1137/S1052623499357258
[21] DOI: 10.1007/s101070100244 · Zbl 1049.90088 · doi:10.1007/s101070100244
[22] DOI: 10.1137/S105262340038081X · Zbl 1029.65063 · doi:10.1137/S105262340038081X
[23] DOI: 10.1137/S1052623401399320 · Zbl 1079.90129 · doi:10.1137/S1052623401399320
[24] DOI: 10.1007/BF00940345 · Zbl 0632.90059 · doi:10.1007/BF00940345
[25] DOI: 10.1007/BF00927673 · Zbl 0174.20705 · doi:10.1007/BF00927673
[26] DOI: 10.1007/BF00940052 · Zbl 0794.90064 · doi:10.1007/BF00940052
[27] DOI: 10.1137/0802027 · Zbl 0761.90089 · doi:10.1137/0802027
[28] DOI: 10.1137/0312021 · Zbl 0257.90046 · doi:10.1137/0312021
[29] DOI: 10.1007/s10107-003-0491-6 · Zbl 1146.90525 · doi:10.1007/s10107-003-0491-6
[30] DOI: 10.1137/S1052623403426556 · Zbl 1114.90128 · doi:10.1137/S1052623403426556
[31] DOI: 10.1007/s10107-004-0559-y · Zbl 1134.90542 · doi:10.1007/s10107-004-0559-y
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.