I. Poser, Poser k ? k + 1 ; Choisir i k ? I F

P. Si, P k2 ) n'a pas de solution, +? (? 2 := +?, resp.)

H. Aussi and . Est, D` es lors, leprobì eme (DC01a) ou bien (DC01b) estéquivalentestéquivalent auprobì eme DC suivant : min{G(x, y) ? H(x, y) : (x, y)

. Maintenant, 9) par DCA. 8.6. Conclusion Instance VarBin VarLin Contr UB CPU Iter LB, p.31

E. H. Aghezzaf, B. Raa, and H. V. Landeghem, Modeling inventory routing problems in supply chains of high consumption products, European Journal of Operational Research, vol.169, issue.3, pp.1048-1063, 2006.
DOI : 10.1016/j.ejor.2005.02.008

R. Bhatia and M. Kodialam, On power efficient communication over multi-hop wireless networks: joint routing, scheduling and power control, IEEE INFOCOM 2004, pp.1457-1466, 2004.
DOI : 10.1109/INFCOM.2004.1357030

P. R. Chandler, M. Pachter, S. R. Rasmussen, and C. Schumacher, Multiple Task Assignment for a UAV Team, AIAA Guidance, Navigation, and Control Conference and Exhibit, 2002.
DOI : 10.2307/2372560

J. Chang and L. Tassiulas, Energy conserving routing in wireless ad-hoc networks, Proc. IEEE INFOCOM-00, pp.21-31, 2000.

L. Chen, S. H. Low, M. Chiang, and J. C. Doyle, Cross-Layer Congestion Control, Routing and Scheduling Design in Ad Hoc Wireless Networks, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications, pp.1-13, 2006.
DOI : 10.1109/INFOCOM.2006.142

T. W. Chien, A. Balakrishnan, and R. T. Wong, An Integrated Inventory Allocation and Vehicle Routing Problem, Transportation Science, vol.23, issue.2, pp.67-76, 1989.
DOI : 10.1287/trsc.23.2.67

C. W. Commander and P. M. Pardalos, A combinatorial algorithm for the TDMA message scheduling problem, Computational Optimization and Applications, vol.29, issue.2, 2006.
DOI : 10.1007/978-1-4615-2025-2

R. L. Cruz and A. V. Santhanam, Optimal routing, link scheduling and power control in multihop wireless networks, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428), pp.702-711, 2003.
DOI : 10.1109/INFCOM.2003.1208720

J. B. Cruz, J. , G. Chen, D. Li, and X. Wang, Particle Swarm Optimization for Resource Allocation in UAV Cooperative Control, AIAA Guidance, Navigation, and Control Conference and Exhibit, 2004.
DOI : 10.1287/opre.45.5.662

M. E. Dyer and L. A. Wolsey, Formulating the single machine sequencing problem with release dates as a mixed integer program, Discrete Applied Mathematics, vol.26, issue.2-3, pp.255-270, 1990.
DOI : 10.1016/0166-218X(90)90104-K

T. Elbatt and A. Ephremides, Joint scheduling and power control for wireless ad hoc networks, Proc. IEEE INFOCOM-02, pp.976-984, 2002.

J. E. Falk and R. M. Soland, An Algorithm for Separable Nonconvex Programming Problems, Management Science, vol.15, issue.9, pp.550-569, 1969.
DOI : 10.1287/mnsc.15.9.550

A. Federgruen and P. Zipkin, A Combined Vehicle Routing and Inventory Allocation Problem, Operations Research, vol.32, issue.5, pp.1019-1037, 1984.
DOI : 10.1287/opre.32.5.1019

R. E. Gomory, An Algorithm for the Mixed Integer Problem, RM-2597, The Rand Corporation, 1960.

R. L. Graham, E. L. Lawler, J. K. Lenstra, and A. H. Kan, Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey, Annals of Discrete Mathematics, vol.5, pp.287-326, 1979.
DOI : 10.1016/S0167-5060(08)70356-X

H. Tuy, Global minimization of a difference of two convex functions, Mathematics Programming Study Acta Mathematica Vietnamica, vol.30, issue.8, pp.150-182, 1983.
DOI : 10.1007/BFb0121159

H. Tuy and D. Optimisation, Theory, Methods and Algorithms, Handbook of Global Optimisation Horst and Pardalos eds, pp.149-216, 1995.

H. Tuy, T. V. Thieu, and N. Q. Thai, A Conical Algorithm for Globally Minimizing a Concave Function Over a Closed Convex Set, Mathematics of Operations Research, vol.10, issue.3, pp.498-514, 1985.
DOI : 10.1287/moor.10.3.498

R. Horst, Deterministic global optimization with partition sets whose feasibility is not known: Application to concave minimization, reverse convex constraints, DC-programming, and Lipschitzian optimization, Journal of Optimization Theory and Applications, vol.34, issue.1, pp.11-37, 1988.
DOI : 10.1515/9781400873173

R. Horst, A general class of branch-and-bound methods in global optimization with some new approaches for concave minimization, Journal of Optimization Theory and Applications, vol.7, issue.2, pp.271-291, 1986.
DOI : 10.1515/9781400873173

R. Horst, N. Van, T. Benson, and H. , Concave minimization via conical partitions and polyhedral outer approximation, Mathematical Programming, vol.10, issue.1-3, pp.259-274, 1991.
DOI : 10.1007/BF01594938

R. Horst, T. Nguyen, D. Van, and J. Vries, On finding new vertices and redundant constraints in cutting plane algorithms for global optimization, Operations Research Letters, vol.7, issue.2, pp.85-90, 1988.
DOI : 10.1016/0167-6377(88)90071-5

R. Horst, N. V. , and H. Tuy, On a outer approximation concept in global optimisation, Optimization, pp.255-264, 1989.

R. Horst and H. Tuy, Global optimization (Deterministic Approaches, 1996.

R. Horst and H. Tuy, On the convergence of global methods in multiextremal optimization, Journal of Optimization Theory and Applications, vol.5, issue.2, pp.253-271, 1987.
DOI : 10.1007/BF00939434

R. Horst, P. M. Pardalos, and V. T. Nguyen, Introduction to global optimization, 1995.
DOI : 10.1007/978-1-4615-0015-5

H. Jiang, W. Zhuang, and X. Shen, Cross-layer design for resource allocation in 3G wireless networks and beyond, IEEE Communications Magazine, vol.43, issue.12, pp.120-126, 2005.
DOI : 10.1109/MCOM.2005.1561929

B. Kalantari and J. B. Rosen, An Algorithm for Global Minimization of Linearly Constrained Concave Quadratic Functions, Mathematics of Operations Research, vol.12, issue.3, pp.544-561, 1987.
DOI : 10.1287/moor.12.3.544

S. Kim, X. Wang, and M. Madihian, Distributed Joint Routing and Medium Access Control for Lifetime Maximization of Wireless Sensor Networks, IEEE Transactions on Wireless Communications, vol.6, issue.7, pp.2669-2677, 2007.
DOI : 10.1109/TWC.2007.05961

J. , L. Ny, and E. Feron, An Approximation Algorithm for the Curvature-Constrained Travelling Salesman Problem, 43rd Annual Allerton Conference on Communications, Control and Computing, 2005.

H. and L. Thi, Analyse numérique des algorithmes de l'optimisation DC. Approches locale et globale . Codes et simulations numériques en grande dimension. Applications, Thèse de Doctorat de l'Université de Rouen, 1994.

H. and L. Thi, ContributionàContributionà l'optimisation non convexe et l'optimisation globale : Théorie, Algorithmes et Applications HabilitationàHabilitationà Diriger des Recherches, 1997.

H. and L. Thi, An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints Mathematical Programming, Ser. A, vol.87, issue.3, pp.401-426, 2000.

H. and L. Thi, Solving large scale Molecular distance geometry problem by a smoothing technique via the Gaussian transform an DC programming, Journal of Global Optimization, vol.27, pp.375-397, 2003.

H. Le-thi, T. Belghiti, and T. , Pham Dinh A new efficient algorithm based on DC programming and DCA for Clustering In Press, Journal of Global Optimization, 2006.

H. Le-thi and M. , Le Hoai and T. Pham Dinh Optimization based DC programming and DCA for Hierarchical Clustering In Press, Available Online, European Journal of Operational Research, 2006.

H. Le-thi, M. L. Hoai, and T. , Pham Dinh Une nouvelle approche basée sur la programmation DC et DCA pour la classification floue EGC, pp.703-714, 2007.

H. A. Le-thi, T. P. Nguyen, and T. , Pham Dinh A Continuous DC Programming Approach to the Strategic Supply Chain Design Problem from Qualified Partner Set, European Journal of Operational Research, vol.183, issue.3, pp.1000-1012, 2007.

L. Thi, H. A. Ndiaye, B. M. Pham-dinh, and T. , Solving a multimodal transport problem by DC, Proceedings of RIVF'08, IEEE International conference on Research, Innovation and Vision for the future in Computing and Communications Technologies, pp.49-56, 2008.

L. Thi, H. A. Ndiaye, B. M. Pham-dinh, and T. , Models and Simulations for Container Allocation on trains in a rapid transhipment shunting yard by DC Programming and DCA, Third International Conference on Computational Management Science, special invited session, 2006.

L. Thi, H. A. Ndiaye, B. M. Pham-dinh, and T. , Programmation DC et DCA pour Le Dispatching des Véhicules Guidés Automatisés dans un Terminaì a Conteneurs Automatisé, Session spéciale invitée, Conférence conjointe FRANCORO V, pp.241-342, 2007.

H. A. Le-thi, T. V. Nguyen, and . Pham-dinh, (Sweden) special invited session, Combined DCA and New Cutting Plane Techniques for Globally Solving Mixed Linear Programming, SIAM Conference on Optimization, 2005.

H. , L. Thi, and T. , Pham Dinh Solving a class of linearly constrained indefinite quadratic problems by DC algorithms, Journal of Global Optimization, vol.11, pp.253-285, 1997.

H. , L. Thi, and T. , Pham Dinh A Branch-and-Bound method via DC Optimization Algorithm and Ellipsoidal techniques for Box Constrained Nonconvex Quadratic Programming Problems, Journal of Global Optimization, vol.13, pp.171-206, 1998.

H. , L. Thi, and T. , Pham Dinh DC programming approach for large-scale molecular optimization via the general distance geometry problem Nonconvex Optimization and Its Applications 40, Optimization in Computational Chemistry and Molecular Biology : Local and Global Approaches, pp.301-339, 2000.

H. , L. Thi, and T. Pham, Dinh Large Scale Molecular Conformation via the Exact Distance Geometry Problem In Optimization, Lecture Notes in Economics and Mathematical Systems, vol.481, pp.260-277, 2000.

H. , L. Thi, and T. , Pham Dinh DC programming approach and solution algorithm to the multidimensional scaling problem Nonconvex Optimization and Its Applications 53 : In From Local to Global Optimization, pp.231-276, 2001.

H. , L. Thi, and T. , Pham Dinh DC optimization approaches via Markov models for restoration of signals (1-D) and (2-D) Nonconvex Optimization and Its Applications 54 : In Advances in Convex Analysis and Global Optimization, pp.300-317, 2001.

H. A. Le-thi and T. , Pham Dinh A Continuous Approach for Globally Solving Linearly Constrained Quadratic Zero -One Programming Problems. Optimization, pp.93-120, 2001.

H. , L. Thi, and T. , Pham Dinh DC Programming Approach for Multicommodity Network Optimization Problems with Step Increasing Cost Functions Special Issue of, Journal of Global Optimization, vol.22, pp.204-233, 2002.

H. , L. Thi, and T. , Applications : The State of the Art First InternationalWorkshop on Global Constrained Optimization and Constraint Satisfaction, Pham Dinh Dc Programming. Theory, Algorithms Laboratory of Modeling, Optimization & Operations Research, 2002.

H. , L. Thi, and T. , Pham Dinh Large scale molecular optimization from distances matrices by a DC optimization approach SIAM, Journal of Optimization, vol.14, issue.1, pp.77-116, 2003.

H. , L. Thi, and T. , Pham Dinh A new algorithm for solving large scale molecular distance geometry problems, Applied Optimization : in Hight Performance Algorithms and Software for Nonlinear Optimization, pp.276-296, 2003.

H. A. Le-thi and T. , Pham Dinh The DC (Difference of Convex functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems, Annals of Operations Research, vol.133, pp.23-46, 2005.

H. , L. Thi, and T. , Pham Dinh A continuous approach for the concave cost supply problem via DC Programming and DCA to appear in, Discrete Applied Mathematics

H. Le-thi and T. , Towards Tikhonov regularization of non-linear ill-posed problems: a dc programming approach, Comptes Rendus Mathematique, vol.335, issue.12, pp.1073-1078, 2002.
DOI : 10.1016/S1631-073X(02)02611-0

URL : https://hal.archives-ouvertes.fr/hal-01636769

H. Le-thi and T. , Pham Dinh and H. Dinh Nho Solving inverse problems for an elliptic equations by DC (Difference of Convex functions) programming, Journal of Global Optimization, vol.25, pp.407-423, 2003.

H. Le-thi and T. , Pham Dinh and H. Dinh Nho On the ill-posedness of the trust region Subproblem Journal of Inverse and Ill-posed Problems, pp.545-577, 2003.

H. Le-thi and T. , Pham Dinh and N. Huynh Van Exact penalty techniques in DC Programming, 2005.

H. Le-thi and T. , Pham Dinh and M. Le Dung Numerical solution for optimization over the efficient set by DC optimization algorithm Operations Research Letters, pp.117-128, 1996.

H. Le-thi and T. , Pham Dinh and M. Le Dung A combined DC Optimization : Ellipsoidal Branch-and-Bound Algorithm for, Solving Nonconvex Quadratic Programming Problems Journal of Combinatorial Optimization, vol.2, issue.1, pp.9-28, 1998.

H. Le-thi, T. Pham-dinh, and M. L. Dung, Exact penalty in DC Programming, Vietnam Journal of Mathematics, vol.27, issue.2, pp.169-178, 1999.
URL : https://hal.archives-ouvertes.fr/hal-01664702

H. Le-thi and T. , Pham Dinh and M. Le Dung Simplicially Constrained DC Optimization over the Efficient Set and Weakly Efficient Sets Journal of Optimization, Theory and Applications, vol.117, issue.3, pp.503-531, 2003.

H. Le-thi and T. , Pham Dinh and T. Nguyen Van Combination between Local and Global Methods for Solving an Optimization Problem over the, Efficient Set European Journal of Operational Research, vol.142, pp.257-270, 2002.

R. Madan, S. Cui, S. Lall, and A. Goldsmith, Mixed integer-linear programming for link scheduling in interference-limited networks, Proc. of 1st workshop on Resource Allocation in Wireless Networks, Italy, 2005.

R. Madan, S. Cui, S. Lall, and A. Goldsmith, Cross-Layer Design for Lifetime Maximization in Interference-Limited Wireless Sensor Networks, IEEE Transactions on Wireless Communications, vol.5, issue.10, pp.3142-3152, 2006.
DOI : 10.1109/TWC.2006.04770

H. Marchand, A polyhedral study of the mixed knapsack set and its use to solve mixed integer programs, 1998.

H. Marchand, A. Martin, R. Weismantel, and L. Wolsey, Cutting planes in integer and mixed integer programming, Discrete Applied Mathematics, vol.123, issue.1-3
DOI : 10.1016/S0166-218X(01)00348-1

R. M. Murray, Recent Research in Cooperative Control of Multivehicle Systems, Journal of Dynamic Systems, Measurement, and Control, vol.33, issue.5, pp.571-583, 2007.
DOI : 10.1109/TAC.2004.834113

B. M. Ndiaye, T. Pham-dinh, and H. A. Le-thi, Single Straddle Carrier Routing Problem in Port Container Terminals: Mathematical Model and Solving Approaches, Modelling, Computation and Optimization in Information Systems and Management Sciences, pp.21-30, 2008.
DOI : 10.1137/S1052623498342794

URL : https://hal.archives-ouvertes.fr/hal-01664533

G. L. Nemhauser and L. A. Wolsey, A recursive procedure to generate all cuts for 0???1 mixed integer programs, Mathematical Programming, pp.379-390, 1990.
DOI : 10.1007/BF01585752

N. Van, T. , and H. Tuy, Convergent algorithms for minimizing a concave function, Mathematic Operations Research, vol.5, pp.556-566, 1980.

V. V. Nguyen, Méthodes exactes pour l'optimisation DC polyédrale en variables mixtes 0-1 basées sur DCA et nouvelles coupes, Thèse de Doctoral, 2006.

T. Pham, Dinh Elements homoduaux relatifsàrelatifsà un couple de normes (?, ?) Applications au calcul de S ?? (A), 1975.

T. Pham, Dinh Calcul du maximum d'une forme quadratique définie positive sur la boule unité de la norme du max, 1976.

T. Pham, Dinh Algorithms for solving a class of non convex optimization problems. Methods of subgradients Fermat days 85, Mathematics for Optimization, 1986.

T. and P. Dinh, Duality in DC (difference of convex functions) optimization. Subgradient methods Trends in Mathematical Optimization, International Series of Numer Math, vol.84, pp.277-293, 1988.

T. , P. Dinh, and H. Thi, Convex analysis approach to d.c. programming : Theory, Algorithms and Applications Acta Mathematica Vietnamica, dedicated to Professor Hoang Tuy on the occasion of his 70th birthday, pp.289-355, 1997.
URL : https://hal.archives-ouvertes.fr/hal-01664714

K. T. Phan, H. Jiang, C. Tellambura, S. A. Vorobyov, and R. Fan, Joint medium access control, routing and energy distribution in multi-hop wireless networks, under revision, IEEE Trans. Wireless Commun

A. T. Phillips and J. B. Rosen, A parallel algorithm for constrained concave quadratic global minimization, Mathematical Programming, vol.34, issue.2, pp.412-448, 1988.
DOI : 10.1007/BF01589415

S. Ramanathan and E. L. Lloyd, Scheduling algorithms for multihop radio networks, IEEE/ACM Transactions on Networking, vol.1, issue.2, pp.166-177, 1993.
DOI : 10.1109/90.222924

URL : http://www.eecis.udel.edu/~elloyd/papers.d/ramton.pdf

A. Richards, J. Bellingham, M. Tillerson, and J. P. How, Coordination and Control of Multiple UAVs, AIAA Guidance, Navigation, and Control Conference and Exhibit, 2002.
DOI : 10.1109/ACC.2001.946414

A. Richards and J. P. How, Aircraft Trajectory PlanningWith Collision Avoidance Using Mixed Integer Linear Progrmming, 2002.
DOI : 10.1109/acc.2002.1023918

R. T. Rockafellar, Convex Analysis, 1970.
DOI : 10.1515/9781400873173

J. B. Rosen and P. M. Pardalos, Global minimization of large-scale constrained concave quadratic problems by separable programming, Mathematical Programming, vol.226, issue.2, pp.163-174, 1986.
DOI : 10.1007/978-3-642-45567-4_7

A. Salman, I. Ahmad, and S. Madani, Particle swarm optimization for task assignment problem, Microprocessors and Microsystems, vol.26, issue.8, pp.363-371, 2002.
DOI : 10.1016/S0141-9331(02)00053-4

C. Schumacher, P. Chandler, M. Pachter, and L. Pachter, Constrained Optimization for UAV Task Assignmnet, AIAA Guidance, Navigation, and Control Confer-ence, 2004.

F. Sourd, New Exact Algorithms for One-Machine Earliness-Tardiness Scheduling, INFORMS Journal on Computing, vol.21, issue.1, pp.167-175, 2009.
DOI : 10.1287/ijoc.1080.0287

URL : https://hal.archives-ouvertes.fr/hal-01185191

F. Sourd and S. Kedad-sidhoum, Set of instances for Earliness-tardiness scheduling with distinct due dates

F. Sourd and S. Kedad-sidhoum, A faster branch-and-bound algorithm for the earliness-tardiness scheduling problem, Journal of Scheduling, vol.142, issue.1, pp.49-58, 2008.
DOI : 10.1023/A:1013741325877

URL : https://hal.archives-ouvertes.fr/hal-01185214

J. P. Sousa and L. A. Wolsey, A time indexed formulation of non-preemptive single machine scheduling problems, Mathematical Programming, vol.25, issue.1-3, pp.353-367, 1992.
DOI : 10.1007/BF01586059

J. Tang, G. Xue, C. Chandler, and W. Zhang, Link Scheduling With Power Control for Throughput Enhancement in Multihop Wireless Networks, IEEE Transactions on Vehicular Technology, vol.55, issue.3, pp.733-742, 2006.
DOI : 10.1109/TVT.2006.873836

Q. P. Thai, Analyse Numérique des Méthodes d'Optimisation Globale, Codes et Simulations numériques. Applications Thèse de doctorat, 1994.

Q. P. Thai, L. Thi, H. A. Pham, and D. T. , On the global solution of linearly constrained indefinite quadratic minimization problems by decomposition branch and bound method. RAIRO, Recherche Opérationnelle, vol.30, issue.1, pp.31-49, 1996.

V. T. 'kindt and J. C. Billaut, Multicriteria Scheduling :Theory, models and Algorithms, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01023714

M. Van-den-akker, H. Hoogeveen, S. Velde, and . Van-de, Combining Column Generation and Lagrangean Relaxation to Solve a Single-Machine Common Due Date Problem, INFORMS Journal on Computing, vol.14, issue.1, pp.35-51, 2002.
DOI : 10.1287/ijoc.14.1.37.7706

A. F. Veinott, The Supporting Hyperplane Method for Unimodal Programming, Operations Research, vol.15, issue.1, pp.147-152, 1967.
DOI : 10.1287/opre.15.1.147

H. Yau, Y. Pan, and L. Shi, New solution approaches to the general single machine earliness tardiness problem, Automation Science and Engineering IEEE Transactions, vol.5, issue.2, pp.349-360, 2008.

Y. Zhong and E. H. Aghezzaf, Analysis and Solution Developement of the Single-Vehicle Inventory Routing Problem, Proc. MCO08, pp.369-407, 2008.
DOI : 10.1023/A:1008652705980

J. Zhu, S. Chen, B. Bensaou, and K. Hung, Tradeoff Between Lifetime and Rate Allocation in Wireless Sensor Networks: A Cross Layer Approach, IEEE INFOCOM 2007, 26th IEEE International Conference on Computer Communications, pp.267-275, 2007.
DOI : 10.1109/INFCOM.2007.39