메뉴 건너뛰기




Volumn 29, Issue 6, 2007, Pages 2507-2530

Implementing generating set search methods for linearly constrained minimization

Author keywords

Constrained optimization; Degeneracy; Derivativefree methods; Direct search; Double description algorithm; Generalized pattern search; Generating set search; Linear constraints; Nonlinear optimization; Nonlinear programming

Indexed keywords

COMPUTATIONAL GEOMETRY; NONLINEAR PROGRAMMING; PROBLEM SOLVING;

EID: 55549119629     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/050635432     Document Type: Article
Times cited : (87)

References (31)
  • 1
    • 34249842390 scopus 로고
    • A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
    • D. M. AVIS AND K. FUKUDA, A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra, Discrete Comput. Geom., 8 (1992), pp. 295-313.
    • (1992) Discrete Comput. Geom , vol.8 , pp. 295-313
    • AVIS, D.M.1    FUKUDA, K.2
  • 2
    • 0001755947 scopus 로고    scopus 로고
    • How good are convex hull algorithms?
    • D. AVIS, D. BREMNER, AND R. SEIDEL, How good are convex hull algorithms?, Comput. Geom., 7 (1997), pp. 265-301.
    • (1997) Comput. Geom , vol.7 , pp. 265-301
    • AVIS, D.1    BREMNER, D.2    SEIDEL, R.3
  • 3
    • 55549120662 scopus 로고    scopus 로고
    • D. AVIS, Irs: A revised implementation of the reverse search vertex enumeration algorithm, in Polytopes - Combinatorics and Computation, G. Kalai and G. Ziegler, eds., Birkhauser-Verlag, Basel, Switzerland, 2000, pp. 177-198.
    • D. AVIS, Irs: A revised implementation of the reverse search vertex enumeration algorithm, in Polytopes - Combinatorics and Computation, G. Kalai and G. Ziegler, eds., Birkhauser-Verlag, Basel, Switzerland, 2000, pp. 177-198.
  • 4
    • 84968510937 scopus 로고
    • A class of methods for solving nonlinear simultaneous equations
    • C. G. BROYDEN, A class of methods for solving nonlinear simultaneous equations, Math. Comput., 19 (1965), pp. 577-593.
    • (1965) Math. Comput , vol.19 , pp. 577-593
    • BROYDEN, C.G.1
  • 6
    • 0030303858 scopus 로고    scopus 로고
    • Convergence properties of an augmented Lagrangian algorithm for optimization with a combination of general equality and linear constraints
    • A. R. CONN, N. GOULD, A. SARTENAER, AND P. L. TOINT, Convergence properties of an augmented Lagrangian algorithm for optimization with a combination of general equality and linear constraints, SIAM J. Optim., 6 (1996), pp. 674-703.
    • (1996) SIAM J. Optim , vol.6 , pp. 674-703
    • CONN, A.R.1    GOULD, N.2    SARTENAER, A.3    TOINT, P.L.4
  • 7
    • 0001605378 scopus 로고
    • Theory of positive linear dependence
    • C. DAVIS, Theory of positive linear dependence, Amer. J. Math., 76 (1954), pp. 733-746.
    • (1954) Amer. J. Math , vol.76 , pp. 733-746
    • DAVIS, C.1
  • 8
    • 2442576133 scopus 로고    scopus 로고
    • On the local convergence properties of pattern search
    • E. D. DOLAN, R. M. LEWIS, AND V. TORCZON, On the local convergence properties of pattern search, SIAM J. Optim., 14 (2003), pp. 567-583.
    • (2003) SIAM J. Optim , vol.14 , pp. 567-583
    • DOLAN, E.D.1    LEWIS, R.M.2    TORCZON, V.3
  • 9
    • 84947909628 scopus 로고    scopus 로고
    • Double description method revisited
    • Combinatorics and Computer Science, M. Deza, R. Euler, and I. Manoussakis, eds, Springer-Verlag, Berlin
    • K. FUKUDA AND A. PRODON, Double description method revisited, in Combinatorics and Computer Science, M. Deza, R. Euler, and I. Manoussakis, eds., Lecture Notes in Comput. Sci. 1120, Springer-Verlag, Berlin, 1997, pp. 91-111.
    • (1997) Lecture Notes in Comput. Sci , vol.1120 , pp. 91-111
    • FUKUDA, K.1    PRODON, A.2
  • 10
    • 55549104847 scopus 로고    scopus 로고
    • K. FUKUDA, cdd/cdd+ Reference Manual, The Institute for Operations Research, ETHZentrum, Zurich, Switzerland, 2005. Available at ftp://ftp.ifor.math.ethz.ch/pub/fukuda/cdd/cddman/cddman.
    • K. FUKUDA, cdd/cdd+ Reference Manual, The Institute for Operations Research, ETHZentrum, Zurich, Switzerland, 2005. Available at ftp://ftp.ifor.math.ethz.ch/pub/fukuda/cdd/cddman/cddman.
  • 11
    • 70450139682 scopus 로고    scopus 로고
    • cdd home
    • K. FUKUDA, cddlib, http://www.ifor.math.ethz.ch/~fukuda/ cdd home/, 2005.
    • (2005) cddlib
    • FUKUDA, K.1
  • 12
    • 0040165653 scopus 로고
    • Theory of convex polyhedral cones
    • Activity Analysis of Production and Allocation, T. C. Koopmans, ed, John Wiley & Sons, New York
    • M. GERSTENHABER, Theory of convex polyhedral cones, in Activity Analysis of Production and Allocation, T. C. Koopmans, ed., Cowles Commission Monograph No. 13, John Wiley & Sons, New York, 1951, pp. 298-316.
    • (1951) Cowles Commission Monograph , vol.13 , pp. 298-316
    • GERSTENHABER, M.1
  • 14
    • 2442598318 scopus 로고    scopus 로고
    • N. I. M. GOULD, D. ORBAN, AND P. L. TOINT, CUTEr (and SifDec), a constrained and unconstrained testing environment, revisited, ACM Transactions on Mathematical Software, 29 (2003), pp. 373-394. See also http://cuter.rl.ac.uk/cuter-www/.
    • N. I. M. GOULD, D. ORBAN, AND P. L. TOINT, CUTEr (and SifDec), a constrained and unconstrained testing environment, revisited, ACM Transactions on Mathematical Software, 29 (2003), pp. 373-394. See also http://cuter.rl.ac.uk/cuter-www/.
  • 15
    • 55549133064 scopus 로고    scopus 로고
    • 2.0, Technical report SAND2000-8843, Sandia National Laboratories, Livermore, CA 94550
    • P. D. HOUGH, T. G. KOLDA, AND H. A. PATRICK, Usage manual for APPSPACK 2.0, Technical report SAND2000-8843, Sandia National Laboratories, Livermore, CA 94550, 2000.
    • (2000) Usage manual for APPSPACK
    • HOUGH, P.D.1    KOLDA, T.G.2    PATRICK, H.A.3
  • 16
    • 0242667172 scopus 로고    scopus 로고
    • Optimization by direct search: New perspectives on some classical and modern methods
    • T. G. KOLDA, R. M. LEWIS, AND V. TORCZON, Optimization by direct search: New perspectives on some classical and modern methods, SIAM Rev., 45 (2003), pp. 385-482.
    • (2003) SIAM Rev , vol.45 , pp. 385-482
    • KOLDA, T.G.1    LEWIS, R.M.2    TORCZON, V.3
  • 17
    • 36249014866 scopus 로고    scopus 로고
    • Stationarity results for generating set search for linearly constrained optimization
    • T. G. KOLDA, R. M. LEWIS, AND V. TORCZON, Stationarity results for generating set search for linearly constrained optimization, SIAM J. Optim., 17 (2006), pp. 943-968.
    • (2006) SIAM J. Optim , vol.17 , pp. 943-968
    • KOLDA, T.G.1    LEWIS, R.M.2    TORCZON, V.3
  • 18
    • 0003686336 scopus 로고    scopus 로고
    • Rank ordering and positive bases in pattern search algorithms
    • Technical report 96-71, Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA
    • R. M. LEWIS AND V. TORCZON, Rank ordering and positive bases in pattern search algorithms, Technical report 96-71, Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA, 1996.
    • (1996)
    • LEWIS, R.M.1    TORCZON, V.2
  • 19
    • 0033412824 scopus 로고    scopus 로고
    • Pattern search algorithms for bound constrained minimization
    • R. M. LEWIS AND V. TORCZON, Pattern search algorithms for bound constrained minimization, SIAM J. Optim., 9 (1999), pp. 1082-1099.
    • (1999) SIAM J. Optim , vol.9 , pp. 1082-1099
    • LEWIS, R.M.1    TORCZON, V.2
  • 20
    • 0034412352 scopus 로고    scopus 로고
    • Pattern search methods for linearly constrained minimization
    • R. M. LEWIS AND V. TORCZON, Pattern search methods for linearly constrained minimization, SIAM J. Optim., 10 (2000), pp. 917-941.
    • (2000) SIAM J. Optim , vol.10 , pp. 917-941
    • LEWIS, R.M.1    TORCZON, V.2
  • 21
    • 0242598302 scopus 로고    scopus 로고
    • Objective-derivative-free methods for constrained optimization
    • S. LUCIDI, M. SCIANDRONE, AND P. TSENG, Objective-derivative-free methods for constrained optimization, Math. Program., 92 (2002), pp. 37-59.
    • (2002) Math. Program , vol.92 , pp. 37-59
    • LUCIDI, S.1    SCIANDRONE, M.2    TSENG, P.3
  • 22
    • 0036471915 scopus 로고    scopus 로고
    • A derivative-free algorithm for bound constrained optimization
    • S. LUCIDI AND M. SCIANDRONE, A derivative-free algorithm for bound constrained optimization, Comput. Optim. Appl., 21 (2002), pp. 119-142.
    • (2002) Comput. Optim. Appl , vol.21 , pp. 119-142
    • LUCIDI, S.1    SCIANDRONE, M.2
  • 24
    • 0001650577 scopus 로고
    • Décomposition orthgonale d'un espace hilbertien selon deux côones mutuellement polaires
    • J.-J. MOREAU, Décomposition orthgonale d'un espace hilbertien selon deux côones mutuellement polaires, C. R. Acad. Sci. Paris, 255 (1962), pp. 238-240.
    • (1962) C. R. Acad. Sci. Paris , vol.255 , pp. 238-240
    • MOREAU, J.-J.1
  • 26
    • 0002043078 scopus 로고
    • The double description method
    • H. Kuhn and A. W.Tucker, eds, Princeton University Press, Princeton, NJ
    • T. S. MOTZKIN, H. RAIFFA, G. THOMPSON, AND R. M. THRALL, The double description method, in Contributions to Theory of Games 2, H. Kuhn and A. W.Tucker, eds., Princeton University Press, Princeton, NJ, 1953.
    • (1953) Contributions to Theory of Games , vol.2
    • MOTZKIN, T.S.1    RAIFFA, H.2    THOMPSON, G.3    THRALL, R.M.4
  • 27
    • 55549101051 scopus 로고    scopus 로고
    • B. A. MURTAGH AND M. A. SAUNDERS, MINOS 5.5 user's guide, Technical report SOL 83-20R, Department of Operations Research, Stanford University, Palo Alto, CA, 1983. Revised 1998.
    • B. A. MURTAGH AND M. A. SAUNDERS, MINOS 5.5 user's guide, Technical report SOL 83-20R, Department of Operations Research, Stanford University, Palo Alto, CA, 1983. Revised 1998.
  • 29
    • 2442449774 scopus 로고
    • A direct search method by the local positive basis for linearly constrained optimization
    • W. YU AND Y. LI, A direct search method by the local positive basis for linearly constrained optimization, Chinese Ann. Math., 2 (1981), pp. 139-146.
    • (1981) Chinese Ann. Math , vol.2 , pp. 139-146
    • YU, W.1    LI, Y.2
  • 31
    • 0002130882 scopus 로고
    • Projections on convex sets in Hilbert space and spectral theory
    • Analysis, E. H. Zarantonello, ed, Academic Press, London and New York
    • E. H. ZARANTONELLO, Projections on convex sets in Hilbert space and spectral theory, in Contributions to Nonlinear Functional Analysis, E. H. Zarantonello, ed., Academic Press, London and New York, 1971, pp. 237-424.
    • (1971) Contributions to Nonlinear Functional , pp. 237-424
    • ZARANTONELLO, E.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.