zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Interior-point methods for nonconvex nonlinear programming: Regularization and warmstarts. (English) Zbl 1181.90243
Summary: In this paper, we investigate the use of an exact primal-dual penalty approach within the framework of an interior-point method for nonconvex nonlinear programming. This approach provides regularization and relaxation, which can aid in solving ill-behaved problems and in warmstarting the algorithm. We present details of our implementation within the loqo algorithm and provide extensive numerical results on the CUTEr test set and on warmstarting in the context of quadratic, nonlinear, mixed integer nonlinear, and goal programming.

90C30Nonlinear programming
90C51Interior-point methods
Full Text: DOI
[1] Anitescu, M.: Nonlinear programs with unbounded Lagrange multiplier sets. Technical Report ANL/MCS-P793-0200, Argonne National Labs
[2] Benson, H.Y.: Numerical testing results for the primal-dual penalty approach. http://www.pages.drexel.edu/$\sim$hvb22/penaltyweb
[3] Benson, H.Y., Shanno, D.F.: An exact primal-dual penalty method approach to warmstarting interior-point methods for linear programming. Comput. Optim. Appl. (2006, to appear) · Zbl 1171.90546
[4] Benson, H.Y., Shanno, D.F., Vanderbei, R.J.: A comparative study of large scale nonlinear optimization algorithms. In: Proceedings of the Workshop on High Performance Algorithms and Software for Nonlinear Optimization, Erice, Italy (2001) · Zbl 1066.90138
[5] Benson, H.Y., Shanno, D.F., Vanderbei, R.J.: Interior-point methods for nonconvex nonlinear programming: filter methods and merit functions. Comput. Optim. Appl. 23(2), 257--272 (2002) · Zbl 1022.90017 · doi:10.1023/A:1020533003783
[6] Benson, H.Y., Shanno, D.F., Vanderbei, R.J.: Interior-point methods for nonconvex nonlinear programming: jamming and comparative numerical testing. Math. Program. A 99(1), 35--48 (2004) · Zbl 1055.90068 · doi:10.1007/s10107-003-0418-2
[7] Benson, H.Y., Sen, A., Shanno, D.F., Vanderbei, R.J.: Interior point algorithms, penalty methods and equilibrium problems. Comput. Optim. Appl. 34(2), 155--182 (2006) · Zbl 1121.90124 · doi:10.1007/s10589-005-3908-8
[8] Bussieck, M.R., Drud, A.S., Meeraus, A.: MINLPLib--a collection of test models for mixed-integer nonlinear programming. INFORMS J. Comput. 15(1), 114--119 (2003) · Zbl 1238.90104 · doi:10.1287/ijoc.
[9] Fiacco, A.V., McCormick, G.P.: Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Research Analysis Corporation, McLean (1968). Republished in 1990 by SIAM, Philadelphia · Zbl 0193.18805
[10] Fletcher, R.: Practical Methods of Optimization. Wiley, Chichester (1987) · Zbl 0905.65002
[11] Gill, P.E., Murray, W., Saunders, M.A.: User’s guide for SNOPT 5.3: a Fortran package for large-scale nonlinear programming. Technical Report, Systems Optimization Laboratory, Stanford University, Stanford, CA (1997)
[12] Gould, N.I.M., Orban, D., Toint, P.L.: An interior-point l1-penalty method for nonlinear optimization. Technical Report RAL-TR-2003-022, Rutherford Appleton Laboratory Chilton, Oxfordshire, UK (November 2003)
[13] Gould, N.I.M., Orban, D., Toint, P.L.: CUTEr and SifDec: a constrained and unconstrained testing environment, revisited. ACM Trans. Math. Softw. 29(4), 373--394 (2003) · Zbl 1068.90526 · doi:10.1145/962437.962439
[14] Hock, W., Schittkowski, K.: Test Examples for Nonlinear Programming Codes. Lecture Notes in Economics and Mathematical Systems, vol. 187. Springer, Heidelberg (1981) · Zbl 0452.90038
[15] Kuriger, G., Ravindran, A.R.: Intelligent search methods for nonlinear goal programming problems. INFOR: Inf. Syst. Oper. Res. 43(2), 79--92 (2005)
[16] Leyffer, S., Lopez-Calva, G., Nocedal, J.: Interior methods for mathematical programs with complementarity constraints. Technical Report OTC 2004-10, Northwestern University, Evanston, IL (December 2004) · Zbl 1112.90095
[17] Matsumoto, M., Nishimura, T.: Mersenne twister: a 623-dimensionally equidistributed uniform pseudorandom number generator. ACM Trans. Model. Comput. Simul. 8(1), 3--30 (1998) · Zbl 0917.65005 · doi:10.1145/272991.272995
[18] Nocedal, J., Waltz, R.A.: Knitro 2.0 user’s manual. Technical Report OTC 02-2002, Optimization Technology Center, Northwestern University (January 2002)
[19] Nocedal, J., Morales, J.L., Waltz, R., Liu, G., Goux, J.P.: Assessing the potential of interior-point methods for nonlinear optimization. Technical Report OTC-2001-6, Optimization Technology Center (2001) · Zbl 1062.65063
[20] Shanno, D.F., Vanderbei, R.J.: Interior-point methods for nonconvex nonlinear programming: orderings and higher-order methods. Math. Program. 87(2), 303--316 (2000) · Zbl 1054.90091 · doi:10.1007/s101070050116
[21] Ulbrich, M., Ulbrich, S., Vicente, L.: A globally convergent primal-dual interior point filter method for nonconvex nonlinear programming. Math. Program. 100, 379--410 (2004) · Zbl 1070.90110 · doi:10.1007/s10107-003-0477-4
[22] Vanderbei, R.J.: AMPL models. http://orfe.princeton.edu/$\sim$rvdb/ampl/nlmodels
[23] Vanderbei, R.J., Shanno, D.F.: An interior-point algorithm for nonconvex nonlinear programming. Comput. Optim. Appl. 13, 231--252 (1999) · Zbl 1040.90564 · doi:10.1023/A:1008677427361
[24] Wächter, A., Biegler, L.: Failure of global convergence for a class of interior point methods for nonlinear programming. Math. Program. 88(3), 565--587 (2000) · Zbl 0963.65063 · doi:10.1007/PL00011386
[25] Wächter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Technical Report RC 23149, IBM T.J. Watson Research Center, Yorktown, USA (March 2004)