×
Guignard, Monique

An homage to Joseph-Louis Lagrange and Pierre Huard. (En hommage à Joseph-Louis Lagrange et à Pierre Huard.) (English) Zbl 1213.01018

Ann. Oper. Res. 149, 103-116 (2007).

MSC:

01A45 History of mathematics in the 17th century
90-03 History of operations research and mathematical programming
Cite Review PDF
Full Text: DOI

References:

[1] Ahn, S. (1996). On Solving Some Optimization Problems in Stochastic and Integer Programming with Applications in Finance and Banking. Ph.D. dissertation, University of Pennsylvania, OPIM Department.
[2] Ahn, S., L. Contesse, and M. Guignard. (latest revision March 2006). ”A Proximal Augmented Lagrangean Relaxation for Linear and Nonlinear Integer Programming.” OPIM Department Report, University of Pennsylvania.
[3] Andalaft, N., P. Andalaft, M. Guignard, A. Magendzo, A. Wainer, and A. Weintraub. (2003). ”A Problem of Forest Harvesting and Road Building.” Operations Research, 51(4), 613–628. · Zbl 1165.90554 · doi:10.1287/opre.51.4.613.16107
[4] Balakrishnan, A., T.L. Magnanti, and Richard T. Wong. (1989). ”A Dual-Ascent Procedure for Large-Scale Uncapacitated Network Design.” Operations Research, 37, 716–740. · Zbl 0681.90083 · doi:10.1287/opre.37.5.716
[5] Bilde, O. and J. Krarup. (1977). ”Sharp Lower Bounds and Efficient Algorithms for the Simple Plant Location Problem.” Annals of Discrete Mathematics, 1, 79–97. · Zbl 0364.90068
[6] Bowman Edward H. (1956). ”Production Scheduling by the Transportation Method of Linear Programming.” Operations Research, 4(1), 100–103. · doi:10.1287/opre.4.1.100
[7] Boyd, S. and L. El Ghaoui. (1993). ”Method of Centers for Minimizing Generalized Eigenvalues.” Linear Algebra and Applications, Special Issue on Systems & Control, 188, 63–111, · Zbl 0781.65051
[8] Broise, P., P. Huard, and J. Sentenac. (1968). Decomposition Des Programmes Mathematiques. Monographies de Recherche Opérationnelle, Dunod, Paris. · Zbl 0155.28301
[9] Caron, R.J., H.J. Greenberg, and A.G. Holder. (2002). ”Analytic Centers and Repelling Inequalities.” European Journal of Operational Research, 144, 268–290. · Zbl 1058.90075 · doi:10.1016/S0377-2217(02)00326-0
[10] Chajakis E. and M. Guignard. (1994). ”The Setup Knapsack Problem.” In S. Martello (Ed.), INFOR, Special Issue on Knapsack Problems, 124–142. · Zbl 0811.90072
[11] Chajakis E. and M. Guignard. (2003). ”Scheduling Deliveries for Vehicles with Multiple Compartments.” Journal of Global Optimization, special issue on Supply Chain Optimization, 26(1), 43–78. · Zbl 1053.90006 · doi:10.1023/A:1023067016014
[12] Chen, B. and M. Guignard. (1998). ”Polyhedral Analysis and Decompositions for Capacitated Plant Location-Type Problems.” Discrete Applied Mathematics, 82, 79–91. · Zbl 0897.90153 · doi:10.1016/S0166-218X(97)00096-6
[13] Cosnard M., Y. Robert, and D. Trystram. (1986). ”Résolution Parallèle De Systèmes Linéaires Denses Par Diagonalisation.” E.D.F. Bulletin de la Direction des Etudes et des Recherches C(2), 67–87. · Zbl 0625.65021
[14] Dekker T.J. and W. Hoffmann. (1989). ”Rehabilitation of the Gauss-Jordan Algorithm.” Nümerische Mathematik, 54, 591–599. · Zbl 0672.65011 · doi:10.1007/BF01396364
[15] Dekker T.J., W. Hoffmann, and K. Potma. (1994). ”Parallel Algorithms for Solving Large Linear Systems.” Journal of Computational and Applied Mathematics, 50, 221–232. · Zbl 0808.65020 · doi:10.1016/0377-0427(94)90302-6
[16] Dekker T.J., W. Hoffmann, and K. Potma. (1997). ”Stability of the Gauss-Huard Algorithm with Partial Pivoting.” Computing, 58(3), 225–244. · Zbl 0881.65019 · doi:10.1007/BF02684391
[17] de Matta, R. (1989). On Solving Production Scheduling Problems with Changeover Cost Using Lagrangean Relaxation. Ph.D. dissertation, Dept. of Decision Sciences, the University of Pennsylvania.
[18] de Matta, R. and M. Guignard. (1994). Dynamic Production Scheduling for A Process Industry. Operations Research, 42(3), 1–12. · Zbl 0809.90066 · doi:10.1287/opre.42.3.492
[19] Denel, J., J.-C. Fiorot, and P. Huard. (1979). ”Maximisation D’une Fonction Concave Linéaire Par Morceaux, Cas Sans Et Avec Contraintes, Méthode Finie De La Plus Forte Pente.” Research Report ANO-004, Université des sciences et technologies de Lille (Lille-1).
[20] Denel, J., J.-C. Fiorot, and P. Huard. (1981). ”The Steepest Ascent Method for the Linear Programming Problem.” RAIRO Analyse Numerique, 15(3), 195–200. · Zbl 0476.90057
[21] Dietrich, B.L. and L.F. Escudero. (1993). ”On modelling the Maximum Workload Allocation for Parallel Unrelated Machines with Setups.” Annals of Operations Research, 43(1–4), 359–77. · Zbl 0783.90049
[22] Dodu, J.-C. and P. Huard. (1988). ”Algorithme à pénalisation simple : méthode quadratique séquentielle non réalisable à convergence globale.” Rapport de recherche/INRIA, RR 0925, 0249–6399.
[23] Dodu, J.-C. and P. Huard. (1990). ”Méthodes de Quasi-Newton en Optimisation Non Linaire.” EDF, HR.30–2245. 96 pages.
[24] Dodu, J.-C. and P. Huard. (1993). Quasi-Newton Methods in Nonlinear Optimization. Research Report 93NJ00024, EDF, Direction des études et de la recherche (Clamart). · Zbl 0612.90091
[25] Erlenkotter, D.E. (1978). ”A Dual-Based Procedure for Uncapacitated Facility Location.” Operations Research, 26, 992–1009. · Zbl 0422.90053 · doi:10.1287/opre.26.6.992
[26] Escudero, L.F., M. Guignard, and K. Malik. (1994). ”A Langrangian Relax-and-Cut Approach for the Sequential Ordering Problem with Precedence Relationships.” In C. Ribeiro (Ed.) Annals of Operations Research 50, Applications of Combinatorial Optimization, pp. 219–237. · Zbl 0833.90068
[27] Fiorot, J.-C. and P. Huard. (1974). ”Une approche théorique du problème de linéarisation en programmation mathématique convexe.” Research Report P-042, Université des sciences et technologies de Lille (Lille-1).
[28] Fiorot, J.-C. and P. Huard. (1979). ”Composition and Union of General Algorithms of Optimization.” Mathematical Programming Study, 10, 69–85. · Zbl 0403.90072
[29] Fisher, M.L. (1981). ”The Lagrangian Relaxation Method for Solving Integer Programming Problems.” Management Science, 27 (1), 1–18. · Zbl 0466.90054 · doi:10.1287/mnsc.27.1.1
[30] Fisher, M.L., R. Jaikumar, L.N. van Wassenhove. (1986). ”A Multiplier Adjustment Method for the Generalized Assignment Problem.” Management Science, 32, 1095–1103. · Zbl 0626.90036 · doi:10.1287/mnsc.32.9.1095
[31] Flegel, M.L. and C. Kanzow. (2005). ”On the Guignard Constraint Qualification for Mathematical Programs with Equilibrium Constraints, ” Optimization, 54, 517–534. · Zbl 1147.90397 · doi:10.1080/02331930500342591
[32] Fréville A. and M. Guignard. (1994). ”Relaxations for Minimax Problems.” Investigacion Operativa, 119–138.
[33] Geoffrion, A.M. (1971). ”Duality in Nonlinear Programming.” SIAM Review, 13(1), 1–37. · Zbl 0232.90049 · doi:10.1137/1013001
[34] Geoffrion, A.M. (1974). ”Lagrangean Relaxation and its uses in Integer Programming.” Mathematical Programming Study, 2, 82–114. · Zbl 0395.90056
[35] Geoffrion, A.M. and R. McBride. (1978). ”Lagrangean Relaxation Applied to Capacitated Facility Location Problems.” AIIE Transactions, 10(1), 40–47. · doi:10.1080/05695557808975181
[36] Glover, F. and D. Klingman. (1988). ”Layering Strategies for Creating Exploitable Structure in Linear and Integer Programs.” Mathematical Programming 40, 165–181. · Zbl 0667.90070 · doi:10.1007/BF01580728
[37] Gondzio, J., R. Sarkissian and J.-P. Vial. (2001). ”Parallel Implementation of a Central Decomposition Method for Solving Large Scale Planning Problems.” Computational Optimization and Applications 19, 5–29. · Zbl 1064.90025 · doi:10.1023/A:1011298218729
[38] Gould, F.J. and J.W. Tolle. (1971). ”A Necessary and Sufficient Qualification for Constrained Optimization.” SIAM J. Appl. Math., 20, 164–172. · Zbl 0217.57501 · doi:10.1137/0120021
[39] Guignard, M. (1969). ”Generalized Kuhn-Tucker Conditions for Mathematical Programming Problems in a Banach Space.” SIAM. J. Control, 7(2), 232–241. · Zbl 0182.53101 · doi:10.1137/0307016
[40] Guignard, M. (1970). ”Conditions d’optimalité et Dualité en programmation mathématique.” Cahiers du Bureau Universitaire de Recherche Opérationnelle, Institut de Statistique de l’Université de Paris, Série Recherche, Cahier n. 14, 62 pages.
[41] Guignard, M. (1971). ”Une condition d’optimalité en programmation en nombres entiers.” Revue Francaise d’Informatique et de Recherche Opérationelle, R2, 108–113. · Zbl 0236.90054
[42] Guignard, M. (1988). ”Décomposition Lagrangienne Et Facettes De Polytopes Entiers.” Comptes Rendus de l’Acagemie des Sciences, Paris, France, t. 307, Serie 1, 225–230. · Zbl 0645.90058
[43] Guignard, M. (1993). ”Solving Makespan Minimization Problems with Lagrangean Decomposition.” Discrete Applied Mathematics, 42, 17–29. · Zbl 0778.90026 · doi:10.1016/0166-218X(93)90176-O
[44] Guignard, M. (1994). ”Primal Relaxations for Integer Programming.” VII CLAIO (Latin-Ibero American Conference on Operations Research and Systems Engineering), Santiago, Chile, also OPIM Department Research Report 94-02-01, University of Pennsylvania.
[45] Guignard, M. (1998). ”Efficient Cuts in Lagrangean Relax-and-Cut Schemes.” European Journal of Operational Research, 105(1), 216–223. · Zbl 0957.90091 · doi:10.1016/S0377-2217(97)00034-9
[46] Guignard, M. (2003). ”Lagrangean Relaxation.” TOP,11(2), 151–228. · Zbl 1079.90087 · doi:10.1007/BF02579036
[47] Guignard, M. and S. Kim. (1986). ”Décomposition lagrangienne: un modèle fournissant de meilleures bornes. ” Comptes Rendus de l’Académie des Sciences, Paris, France, t. 303, Serie 1, 667–670. · Zbl 0604.90103
[48] Guignard, M. and S. Kim. (1987). ”Lagrangean Decomposition: A Model Yielding Stronger Bounds.” Mathematical Programming, 39(2), 215–228. · Zbl 0638.90074 · doi:10.1007/BF02592954
[49] Guignard, M. and S. Kim. (1987). ”Lagrangean Decomposition for Integer Programming: Theory and Applications.” RAIRO – RO – Operations Research 21(4), 307–323. · Zbl 0638.90075
[50] Guignard M., C. Ryu, and K. Spielberg. (1998). ”Model Tightening for Integrated Timber Harvest and Transportation Planning.” European J. of Operational Research, 111, 448–460. · Zbl 0938.90007 · doi:10.1016/S0377-2217(97)00362-7
[51] Guignard, M. and M. Rosenwein. (1989). ”An Improved Dual-Based Algorithm for the Generalized Assignment Problem.” Operations Research, 37, 658–663. · Zbl 0674.90068 · doi:10.1287/opre.37.4.658
[52] Guignard, M. and M. Rosenwein. (1990). ”An Application of Lagrangean Decomposition to Resource-Constrained Minimum Weighted Arborescence Problem.” Networks, 20, 345–359. · Zbl 0701.90064 · doi:10.1002/net.3230200306
[53] Guignard, M. and K. Spielberg. (1979). ”A Direct Dual Method for the Mixed Plant Location Problem with Some Side Constraints.” Mathematical Programming, 17, 198–228. · Zbl 0416.90052 · doi:10.1007/BF01588244
[54] Guignard, M. and K. Spielberg. (1981). ”Logical Reduction Methods in 0–1 Programming.” Operations Research, 29(1), 49–74. · Zbl 0452.90044 · doi:10.1287/opre.29.1.49
[55] Gunn, E.A. and A.K. Rai. (1987). ”Modeling and Decomposition for Planning Long-Term Forest Harvesting in an Integrated Industry Structure.” Can. J. For. Res. 17, 1507–1518. · doi:10.1139/x87-233
[56] Held, M. and R.M. Karp. (1970). ”The Traveling-Salesman Problem and Minimum Spanning Trees.” Operations Research, 18, 1138–1162. · Zbl 0226.90047 · doi:10.1287/opre.18.6.1138
[57] Held, M. and R.M. Karp. (1971). ”The Traveling-Salesman Problem and Minimum Spanning Trees: Part II.” Mathematical Programming 1, 6–25. · Zbl 0232.90038 · doi:10.1007/BF01584070
[58] Hoffmann, W. (1998). ”The Gauss-Huard Algorithm and LU Factorization.” Linear Algebra and Its Applications, 275–276, 281–286. · Zbl 0935.65018
[59] Hoffmann, W. and G.G. Pronk. (1994). ”Implementation of Gauss-Huard’s Method on the IBM 9076 SP1.” Technical Report CS-94-03, Department of Computer Systems, Faculty of Mathematics and Computer Science, University of Amsterdam.
[60] Hoffmann, W., K. Potma, and G.G. Pronk. (1994). ”Solving Dense Linear Systems by Gauss-Huard’s Method on a Distributed Memory System.” Future Generation Computer Systems, 10, 321–325. · doi:10.1016/0167-739X(94)90037-X
[61] Huard, P. (1961). ”Sur l’ecriture du maître-programme dans le cas d’un programme satellite décomposé.” Technical report, Note E.D.F. HX 410/365.
[62] Huard, P. (1962). ”Dual Programs.” IBM J. of Res. and Dev., 137–139. · Zbl 0116.12403
[63] Huard, P. (1963a). Convex Programming–Dual Algorithm. Research Report 63–21, O.R. Center, University of California at Berkeley.
[64] Huard, P. (1963b). ”Application Du Principe De Décomposition Aux Programmes Mathématiques Non Linéaires.” Technical report, Note E.D.F. HR 5467.
[65] Huard P. (1964a). ”Mathématiques Des Programmes Economiques.” Monographies de Recherche Opérationnelle, Dunod, Paris.
[66] Huard, P. (1964b). ”Résolution des programmes mathématiques par la méthode des centres.” Technical report, Note E.D.F. HR 5690.
[67] Huard, P. (1967). ”Resolution of Mathematical Programming with Nonlinear Constraints by the Method of Centers.” In J. Abadie, (Ed.), Nonlinear Programming, North Holland, Amsterdam, pp. 207–219. · Zbl 0157.49701
[68] Huard, P. (1970). ”A Method of Centers by Upper-Bounding Functions with Applications.” In J. B. Rosen, O. L. Mangasarian and K. Ritter, (Eds.) Nonlinear Programming, Proceedings of a Symposium held at the University of Wisconsin, Madison, Wisconsin, USA, May 1970, Academic Press, New York, pp. 1–30. · Zbl 0253.90049
[69] Huard, P. (1975a). ”La méthode du gradient projeté dans le cas de contraintes non-linéaires.” Research Report P-058, Université des sciences et technologies de Lille (Lille-1).
[70] Huard, P. (1975b). ”Optimization Algorithms and Point-to-Set Maps.” Mathematical Programming, 8, 308–331. · Zbl 0312.90052 · doi:10.1007/BF01580449
[71] Huard, P. (1976). ”Implementation of Gradient Methods by Tangential Discretization.” Research Report P-073, Université des sciences et technologies de Lille (Lille-1). Appeared in 1979 in JOTA, 28(4), 483–499. · Zbl 0388.65017
[72] Huard, P. (1979a). ”La methode Simplex sans inverse éxplicite.” E. D. F.–Bulletin de la D. E. R., Série C, 2, 79–98.
[73] Huard, P. (1979b). ”La methode de frank ét wolfe ’a petits pas’.” Research Report ANO-007, Université des Sciences et Technologies de Lille (Lille-1).
[74] Huard, P. (1979c). ”Extensions of Zangwill’s Theorem.” Mathematical Programming Study, 10, 98–103. · Zbl 0401.90107
[75] Huard, P. (1981). ”Une approche synthétique des recherches linéaires dans les méthodes de pente.” Research Report ANO-044, Université des Sciences et Technologies de Lille (Lille-1).
[76] Huard, P. (1982). ”Un algorithme général de gradient réduit.” Research Report ANO-066, Université des Sciences et Technologies de Lille (Lille-1). · Zbl 0582.65052
[77] Jörnsten, K.O., M. Näsberg, and P.A. Smeds. (1985). ”Variable Splitting–A New Lagrangean Relaxation Approach to Some Mathematical Programming Models.” Report LiTH-MAT-R-85-04, Department of Mathematics, Linköping Institute of Technology, Sweden.
[78] Karmarkar, U.S. and L. Schrage. (1985). ”The Deterministic Dynamic Product Cycling Problem.” Operations Research, 33(2), 326–345. · Zbl 0571.90038
[79] Karush, W. (1939). ”Minima of Functions of Several Variables with Inequalities as Side Constraints.” M.Sc. dissertation, Dept. of Mathematics, Univ. of Chicago, Chicago, Ill.
[80] Kuhn, H.W. and A.W. Tucker. (1951). ”Nonlinear Programming.” In J. Neyman (Ed.), Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Univ. of California Press, Berkeley, California, pp. 481–492. · Zbl 0044.05903
[81] Laurent-Gengoux, P. and D. Trystram. (1990). ”A New Presentation of the Conjugate Direction Algorithm.” Journal of Computational and Applied Mathematics, 32, 417–422. · Zbl 0722.65010 · doi:10.1016/0377-0427(90)90046-3
[82] Lee, H. and M. Guignard. (1996). ”A Hybrid Bounding Procedure for the Workload Allocation Problem on Parallel Unrelated Machines with Setups.” J. Operational Research Society, 47, 1247–1261. · Zbl 0871.90049
[83] Lieu, B.-T. and P. Huard. (1966). ”La méthode des centres dans un espace topologique.” Nümerische Mathematik, 8, 56–57. · Zbl 0171.40802 · doi:10.1007/BF02165238
[84] Mangasarian, O.L. (1975). ”Second Order and Higher Order Duality in Nonlinear Programming.” J. Math. Anal. Appl., 51 (3), 607–620. · Zbl 0313.90052 · doi:10.1016/0022-247X(75)90111-0
[85] Michelon, P. (1992). Private Communication.
[86] Michelon, P. and N. Maculan. (1992). ”Solving the Lagrangean Dual Problem in Integer Programming.” Department d’Informatique et de Recherche Operationnelle, Université de Montréal, Publication 82. · Zbl 0753.90047
[87] Minoux, M. (1983). ”Lagrangean Decomposition.” Oral communication.
[88] Opaswongkarn, K. (1984). Single and Multi-Commodity Plant Location Problems. Ph.D. dissertation, Dept. of Decision Sciences, the University of Pennsylvania.
[89] Potma, K. and W. Hoffmann. (1994). ”Performance Evaluation of Gauss-Huard’s Method for Hierarchical Memory Systems.” Report CS-94–07, University of Amsterdam (NL). Institute for logic, language and computation.
[90] Reinoso, H. and N. Maculan. (1992). ”Lagrangean Decomposition in Integer Linear Programming: A New Scheme.” INFOR, 30, 1–5. · Zbl 0760.90073
[91] Ribeiro, C. (1983). ”Algorithmes de recherche de plus courts chemins avec contraintes: etude théorique, implémantation et parallélisation.” Doctoral Dissertation, Paris.
[92] Ribeiro, C. and M. Minoux. (1984). ”Solving Hard Constrained Shortest Paths Problems.” ORSA-TIMS Meeting, Dallas. · Zbl 0549.90073
[93] Ribeiro, C. and M. Minoux. (1986). ”Solving Hard Constrained Shortest Paths Problems by Lagrangean Relaxation and Branch-and-Bound Algorithme.” Methods of Operations Research 53, 303–316. · Zbl 0596.90091
[94] Roos, C. (2002). ”Interior-Point Methods for Linear Optimization.” In P. Pardalos and M. Resende, (Eds.) Handbook of Applied Optimization, New York, USA, Oxford University Press, pp. 21–39.
[95] Roos, K. (2004). ”From Linear Optimization to Conic Optimization.” NMC 2004, Tilburg, April 17, 2004, and Seminar, Department of Mathematics, Universitas Padjadjaran, Bandung, Indonesia, August 21, 2004.
[96] Shepardson, F. and R.E. Marsten. (1980). ”A Lagrangean Relaxation Algorithm for the Two Duty Period Scheduling Problem.” Management Science, 26(3), 274–281. · Zbl 0448.90042 · doi:10.1287/mnsc.26.3.274
[97] Trick, M. (1987). ”Networks with Additonal Structured Constraints,” Ph.D. Thesis, School of Industrial and Systems Engineering, Georgia Institute of Technology.
[98] Vajda, S. (1974). ”Test of Optimality.” In P. L. Hammer and G. Zoutendijk, (Eds.) Mathematical programming in theory and practice, Proceedings of the NATO advanced study institute, Figueira da Foz, Portugal, June 12–23, 1972, North-Holland Pub. Co., Amsterdam, ISBN 044410741X.
[99] Yang X.M., X.Q. Yang, and K.L. Teo. (2005). ”Huard Type Second-Order Converse Duality for Nonlinear Programming.” Appl. Math. Lett. 18(2), 205–208. · Zbl 1074.90055 · doi:10.1016/j.aml.2004.04.008
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.