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40 results on '"Goffin, J.-L."'

14. Using central prices in the decomposition of linear programs

Author

Goffin, J.-L., Haurie, A., Vial, J.-Ph., and Zhu, D.L.

Subjects
Linear programming -- Methods, Decomposition (Mathematics) -- Methods, Mathematical optimization -- Methods, Business, Business, general, Business, international
Abstract

A decomposition technique for solving the master program of large structured linear programming problems which offers faster convergence is presented. The technique generates cuts close to the analytic center of the solution set localization resulting in iterations with decreasing set localizations. The effectivity of the technique lies in its use of balanced central prices against conventional optimal price combinations of subproblems.

Published
1993

22. A primal–dual regularized interior-point method for semidefinite programming.

Author

Dehghani, A., Goffin, J.-L., and Orban, D.

Subjects
*DUALITY theory (Mathematics), *SEMIDEFINITE programming, *INTERIOR-point methods, *MATHEMATICAL regularization, *SYMMETRIC matrices
Abstract

Interior-point methods in semidefinite programming (SDP) require the solution of a sequence of linear systems which are used to derive the search directions. Safeguards are typically required in order to handle rank-deficient Jacobians and free variables. We generalize the primal–dual regularization of Friedlander and Orban [A primal–dual regularized interior-point method for convex quadratic programs, Math. Program. Comput. 4 (2012), pp. 71–107] to SDP and show that it is possible to recover an optimal solution of the original primal–dual pair by taking one step of Newton method to a sequence of regularized SDPs at each iteration for both the Nesterov–Todd and dual Helmberg–Kojima–Monteiro (HKM) directions. Computationally, a sparse factorization may be used on a sparse augmented system instead of the more costly symmetric indefinite factorization. Benefits of our approach include increased robustness and a simpler implementation. Our method does not require the constraints to be linearly independent and does not assume that Slater's condition holds. We report numerical experience on standard problems that illustrate our findings. [ABSTRACT FROM AUTHOR]

Published
2017
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23. A Lagrangian Relaxation of the Capacited Multi-Item Lot Sizing Problem Solved with an Interior Point Cutting Plane Algorithm

Author

Du Merle, Olivier, Goffin, J.-L., Trouiller, C., and Vial, Jean-Philippe

Subjects
ddc:332/658
Abstract

The capacitated multi-item lot sizing problem consists of finding a production shedule that minimizes over a finite number of periods the total production, holding inventory, and setup costs subject to demand and capacity constraints. The CLSP problem is NP-hard, while the problem of finding a feasible solution, which is polynomial if there are no set-up times, becomes NP-complete when set-up-times are included. Approximate solution can be obtained by heuristics. In this paper we consider an approach based on a Lagrangian relaxation of the capacity constraints. The relaxation is used in two ways. First, generates a lower bound for the optimal value. Second, the primal and dual solutions of the relaxation (if available) are used to generate integer feasible solutions by primal or dual heuristics. We compare three methods of solving the Lagrangian relaxation: subgradient method, Kelley's cutting plane method - also known as Dantzig-Wolfe decomposition - and the analytic center cutting plane method. We conclude that the analytic center cutting plane method performs as well, and sometimes better than subgradient optimization or Kelley's cuting plane method

Published
1997

29. Conjugate gradient methods for linearly constrained nonlinear programming

Author

Shanno, D. F., Marsten, R. E., Cottle, R. W., editor, Dixon, L. C. W., editor, Korte, B., editor, Magnanti, T. L., editor, Todd, M. J., editor, Allgower, E. L., editor, Bartels, R., editor, Chvatal, V., editor, Dennis, J. E., Jr., editor, Eaves, B. C., editor, Fletcher, R., editor, Hiriart-Urruty, J.- B., editor, Iri, M., editor, Jeroslow, R. G., editor, Johnson, D. S., editor, Lemarechal, C., editor, Lovasz, L., editor, McLinden, L., editor, Padberg, M. W., editor, Powell, M. J. D., editor, Pulleyblank, W. R., editor, Ritter, K., editor, Sargent, R. W. H., editor, Shanno, D. F., editor, Trotter, L. E., Jr., editor, Tuy, H., editor, Wets, R. J. B., editor, Witzgall, C., editor, Beale, E. M. L., editor, Dantzig, G. B., editor, Kantorovich, L. V., editor, Koopmans, T. C., editor, Tucker, A. W., editor, Wolfe, P., editor, Buckley, A. G., editor, and Goffin, J.- L., editor

Published
1982
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30. Asymptotic properties of reduction methods applying linearly equality constrained reduced problems

Author

Van Der Hoek, G., Cottle, R. W., editor, Dixon, L. C. W., editor, Korte, B., editor, Magnanti, T. L., editor, Todd, M. J., editor, Allgower, E. L., editor, Bartels, R., editor, Chvatal, V., editor, Dennis, J. E., Jr., editor, Eaves, B. C., editor, Fletcher, R., editor, Hiriart-Urruty, J.- B., editor, Iri, M., editor, Jeroslow, R. G., editor, Johnson, D. S., editor, Lemarechal, C., editor, Lovasz, L., editor, McLinden, L., editor, Padberg, M. W., editor, Powell, M. J. D., editor, Pulleyblank, W. R., editor, Ritter, K., editor, Sargent, R. W. H., editor, Shanno, D. F., editor, Trotter, L. E., Jr., editor, Tuy, H., editor, Wets, R. J. B., editor, Witzgall, C., editor, Beale, E. M. L., editor, Dantzig, G. B., editor, Kantorovich, L. V., editor, Koopmans, T. C., editor, Tucker, A. W., editor, Wolfe, P., editor, Buckley, A. G., editor, and Goffin, J.- L., editor

Published
1982
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31. A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints

Author

Murtagh, Bruce A., Saunders, Michael A., Cottle, R. W., editor, Dixon, L. C. W., editor, Korte, B., editor, Magnanti, T. L., editor, Todd, M. J., editor, Allgower, E. L., editor, Bartels, R., editor, Chvatal, V., editor, Dennis, J. E., Jr., editor, Eaves, B. C., editor, Fletcher, R., editor, Hiriart-Urruty, J.- B., editor, Iri, M., editor, Jeroslow, R. G., editor, Johnson, D. S., editor, Lemarechal, C., editor, Lovasz, L., editor, McLinden, L., editor, Padberg, M. W., editor, Powell, M. J. D., editor, Pulleyblank, W. R., editor, Ritter, K., editor, Sargent, R. W. H., editor, Shanno, D. F., editor, Trotter, L. E., Jr., editor, Tuy, H., editor, Wets, R. J. B., editor, Witzgall, C., editor, Beale, E. M. L., editor, Dantzig, G. B., editor, Kantorovich, L. V., editor, Koopmans, T. C., editor, Tucker, A. W., editor, Wolfe, P., editor, Buckley, A. G., editor, and Goffin, J.- L., editor

Published
1982
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32. Determining feasibility of a set of nonlinear inequality constraints

Author

Schnabel, Robert B., Cottle, R. W., editor, Dixon, L. C. W., editor, Korte, B., editor, Magnanti, T. L., editor, Todd, M. J., editor, Allgower, E. L., editor, Bartels, R., editor, Chvatal, V., editor, Dennis, J. E., Jr., editor, Eaves, B. C., editor, Fletcher, R., editor, Hiriart-Urruty, J.- B., editor, Iri, M., editor, Jeroslow, R. G., editor, Johnson, D. S., editor, Lemarechal, C., editor, Lovasz, L., editor, McLinden, L., editor, Padberg, M. W., editor, Powell, M. J. D., editor, Pulleyblank, W. R., editor, Ritter, K., editor, Sargent, R. W. H., editor, Shanno, D. F., editor, Trotter, L. E., Jr., editor, Tuy, H., editor, Wets, R. J. B., editor, Witzgall, C., editor, Beale, E. M. L., editor, Dantzig, G. B., editor, Kantorovich, L. V., editor, Koopmans, T. C., editor, Tucker, A. W., editor, Wolfe, P., editor, Buckley, A. G., editor, and Goffin, J.- L., editor

Published
1982
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33. On some experiments which delimit the utility of nonlinear programming methods for engineering design

Author

Sandgren, E., Ragsdell, K. M., Cottle, R. W., editor, Dixon, L. C. W., editor, Korte, B., editor, Magnanti, T. L., editor, Todd, M. J., editor, Allgower, E. L., editor, Bartels, R., editor, Chvatal, V., editor, Dennis, J. E., Jr., editor, Eaves, B. C., editor, Fletcher, R., editor, Hiriart-Urruty, J.- B., editor, Iri, M., editor, Jeroslow, R. G., editor, Johnson, D. S., editor, Lemarechal, C., editor, Lovasz, L., editor, McLinden, L., editor, Padberg, M. W., editor, Powell, M. J. D., editor, Pulleyblank, W. R., editor, Ritter, K., editor, Sargent, R. W. H., editor, Shanno, D. F., editor, Trotter, L. E., Jr., editor, Tuy, H., editor, Wets, R. J. B., editor, Witzgall, C., editor, Beale, E. M. L., editor, Dantzig, G. B., editor, Kantorovich, L. V., editor, Koopmans, T. C., editor, Tucker, A. W., editor, Wolfe, P., editor, Buckley, A. G., editor, and Goffin, J.- L., editor

Published
1982
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34. Computation of the search direction in constrained optimization algorithms

Author

Murray, Walter, Wright, Margaret H., Cottle, R. W., editor, Dixon, L. C. W., editor, Korte, B., editor, Magnanti, T. L., editor, Todd, M. J., editor, Allgower, E. L., editor, Bartels, R., editor, Chvatal, V., editor, Dennis, J. E., Jr., editor, Eaves, B. C., editor, Fletcher, R., editor, Hiriart-Urruty, J.- B., editor, Iri, M., editor, Jeroslow, R. G., editor, Johnson, D. S., editor, Lemarechal, C., editor, Lovasz, L., editor, McLinden, L., editor, Padberg, M. W., editor, Powell, M. J. D., editor, Pulleyblank, W. R., editor, Ritter, K., editor, Sargent, R. W. H., editor, Shanno, D. F., editor, Trotter, L. E., Jr., editor, Tuy, H., editor, Wets, R. J. B., editor, Witzgall, C., editor, Beale, E. M. L., editor, Dantzig, G. B., editor, Kantorovich, L. V., editor, Koopmans, T. C., editor, Tucker, A. W., editor, Wolfe, P., editor, Buckley, A. G., editor, and Goffin, J.- L., editor

Published
1982
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35. A surperlinearly convergent algorithm for constrained optimization problems

Author

Mayne, D. Q., Polak, E., Cottle, R. W., editor, Dixon, L. C. W., editor, Korte, B., editor, Magnanti, T. L., editor, Todd, M. J., editor, Allgower, E. L., editor, Bartels, R., editor, Chvatal, V., editor, Dennis, J. E., Jr., editor, Eaves, B. C., editor, Fletcher, R., editor, Hiriart-Urruty, J.- B., editor, Iri, M., editor, Jeroslow, R. G., editor, Johnson, D. S., editor, Lemarechal, C., editor, Lovasz, L., editor, McLinden, L., editor, Padberg, M. W., editor, Powell, M. J. D., editor, Pulleyblank, W. R., editor, Ritter, K., editor, Sargent, R. W. H., editor, Shanno, D. F., editor, Trotter, L. E., Jr., editor, Tuy, H., editor, Wets, R. J. B., editor, Witzgall, C., editor, Beale, E. M. L., editor, Dantzig, G. B., editor, Kantorovich, L. V., editor, Koopmans, T. C., editor, Tucker, A. W., editor, Wolfe, P., editor, Buckley, A. G., editor, and Goffin, J.- L., editor

Published
1982
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36. Reduced quasi-Newton methods with feasibility improvement for nonlinearly constrained optimization

Author

Gabay, Daniel, Cottle, R. W., editor, Dixon, L. C. W., editor, Korte, B., editor, Magnanti, T. L., editor, Todd, M. J., editor, Allgower, E. L., editor, Bartels, R., editor, Chvatal, V., editor, Dennis, J. E., Jr., editor, Eaves, B. C., editor, Fletcher, R., editor, Hiriart-Urruty, J.- B., editor, Iri, M., editor, Jeroslow, R. G., editor, Johnson, D. S., editor, Lemarechal, C., editor, Lovasz, L., editor, McLinden, L., editor, Padberg, M. W., editor, Powell, M. J. D., editor, Pulleyblank, W. R., editor, Ritter, K., editor, Sargent, R. W. H., editor, Shanno, D. F., editor, Trotter, L. E., Jr., editor, Tuy, H., editor, Wets, R. J. B., editor, Witzgall, C., editor, Beale, E. M. L., editor, Dantzig, G. B., editor, Kantorovich, L. V., editor, Koopmans, T. C., editor, Tucker, A. W., editor, Wolfe, P., editor, Buckley, A. G., editor, and Goffin, J.- L., editor

Published
1982
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37. The watchdog technique for forcing convergence in algorithms for constrained optimization

Author

Chamberlain, R. M., Powell, M. J. D., Lemarechal, C., Pedersen, H. C., Cottle, R. W., editor, Dixon, L. C. W., editor, Korte, B., editor, Magnanti, T. L., editor, Todd, M. J., editor, Allgower, E. L., editor, Bartels, R., editor, Chvatal, V., editor, Dennis, J. E., Jr., editor, Eaves, B. C., editor, Fletcher, R., editor, Hiriart-Urruty, J.- B., editor, Iri, M., editor, Jeroslow, R. G., editor, Johnson, D. S., editor, Lemarechal, C., editor, Lovasz, L., editor, McLinden, L., editor, Padberg, M. W., editor, Powell, M. J. D., editor, Pulleyblank, W. R., editor, Ritter, K., editor, Sargent, R. W. H., editor, Shanno, D. F., editor, Trotter, L. E., Jr., editor, Tuy, H., editor, Wets, R. J. B., editor, Witzgall, C., editor, Beale, E. M. L., editor, Dantzig, G. B., editor, Kantorovich, L. V., editor, Koopmans, T. C., editor, Tucker, A. W., editor, Wolfe, P., editor, Buckley, A. G., editor, and Goffin, J.- L., editor

Published
1982
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