Bazaraa, Mokhtar; Goode, Jamie J. A survey of various tactics for generating Lagrangian multipliers in the context of Lagrangian duality. (English) Zbl 0405.90062 Eur. J. Oper. Res. 3, 322-338 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 36 Documents MSC: 90C30 Nonlinear programming 90C99 Mathematical programming 49M29 Numerical methods involving duality Keywords:Lagrangian Multipliers; Lagrangian Duality; Subdifferentials; Steepest Ascent Directions; Shortest Subgradients PDF BibTeX XML Cite \textit{M. Bazaraa} and \textit{J. J. Goode}, Eur. J. Oper. Res. 3, 322--338 (1979; Zbl 0405.90062) Full Text: DOI OpenURL References: [1] Agmon, S., The relaxation method for linear inequalities, Can. J. math., 6, 382-392, (1954) · Zbl 0055.35001 [2] Balas, E., An infeasibility pricing decomposition method for linear programs, Operations res., 14, 847-873, (1966) · Zbl 0158.38404 [3] () [4] Bazaraa, M.S., Geometry and resolution of duality gaps, Naval res. logist. quart., 20, 357-365, (1973) · Zbl 0262.90056 [5] Bazaraa, M.S.; Goode, J.J., The traveling salesman problem: A duality approach, Mathematical programming, 13, 221-237, (1977) · Zbl 0377.90092 [6] Bazaraa, M.S.; Sherali, H.D., A convergent subgradient optimization scheme, (1978), School of Industrial and Systems Engineering, Georgia Institute of Technology Atlanta, GA [7] Bazaraa, M.S.; Shetty, C.M., Nonlinear programming: theory and algorithms, (1979), John Wiley New York · Zbl 0476.90035 [8] Bazaraa, M.S.; Goode, J.J.; Rardin, R.L., An algorithm for finding the shortest element of a polyhedral set with application to Lagrangian duality, J. math. anal. appl., 65, 278-288, (1978) · Zbl 0383.90073 [9] Bazaraa, M.S.; Goode, J.J.; Rardin, R.L., A finite steepest ascent algorithm for maximizing piecewise-linear concave functions, J. optimization theory appl., 25, 437-442, (1978) · Zbl 0362.90114 [10] Bertsekas, D.P., Nondifferentiable optimization via approximation, (), 1-25 · Zbl 0866.90059 [11] Danskin, J.M., The theory of MAX-MIN with applications, SIAM J. appl. math., 14, 641-664, (1966) · Zbl 0144.43301 [12] Dantzig, G.B.; Wolfe, P., The decomposition algorithm for linear programming, Econometrica, 29, 767-778, (1961) · Zbl 0104.14305 [13] Dantzig, G.B., Linear programming and extensions, (1963), Princeton University Press Princeton, NJ · Zbl 0108.33103 [14] Demyanov, V.F., Algorithms for some minimax problems, J. comput. systems sci., 2, 342-380, (1968) · Zbl 0177.23104 [15] Dzielinski, B.P.; Gomory, R., Optimal programming of lot size inventory and labor allocations, Management sci., 11, 874-890, (1965) [16] Eggleston, H.G., Convexity, (1958), Cambridge University Press Cambridge, MA · Zbl 0086.15302 [17] Everett, H., Generalized Lagrange multiplier method for solving problems of optimum allocation of resources, Operations res., 11, 399-417, (1963) · Zbl 0113.14202 [18] Falk, J.E., Lagrange multipliers and nonlinear programming, J. math. anal., 19, 141-159, (1967) · Zbl 0154.44803 [19] Falk, J.E.; Soland, R.M., An algorithm for separable nonconvex programming problems, Management sci., 15, 550-569, (1969) · Zbl 0172.43802 [20] Fenchel, W., Convex cones, sets, and functions, lecture notes, (1953), Princeton University Press Princeton. NJ · Zbl 0053.12203 [21] Fisher, M.L., Optimal solution of scheduling problems using generalized Lagrange multipliers: part I, Operations res., 11, 1114-1127, (1973) · Zbl 0294.90085 [22] Fisher, M.L., A dual algorithm for the one machine scheduling problem, Mathematical programming, 11, 229-251, (1976) · Zbl 0359.90039 [23] Fisher, M.L.; Northup, W.D.; Shapiro, J.F., Using duality to solve discrete optimization problems: theory and computational experience, (), 56-94 · Zbl 0367.90087 [24] Geoffrion, A.M., Elements of large-scale mathematical programming, Management sci., 10, 652-691, (1970) · Zbl 0209.22801 [25] Geoffrion, A.M., Duality in nonlinear programming: A simplified applications-oriented development, SIAM rev., 13, 1-37, (1971) · Zbl 0232.90049 [26] Geoffrion, A.M., Lagrangian relaxation for integer programming, (), 82-114 · Zbl 0395.90056 [27] Gill, P.E.; Murray, W., Numerical methods for constrainted optimization, (1974), Academic Press New York [28] Grinold, R.C., Steepest ascent for large scale linear programs, SIAM rev., 14, 447-464, (1972) · Zbl 0281.90044 [29] Held, M.; Karp, R.M., The traveling salesman problem and minimum spanning trees, Operations res., 18, 1138-1162, (1970) · Zbl 0226.90047 [30] Held, M.; Karp, R.M., The traveling salesman problem and minimum spanning trees: part II, Mathematical programming, 1, 6-25, (1971) · Zbl 0232.90038 [31] Held, M.; Wolfe, P.; Crowder, H.D., Validation of subgradient optimization, Mathematical programming, 6, 62-88, (1974) · Zbl 0284.90057 [32] Kelley, J.E., The cutting plane method for solving convex programs, SIAM J. appl. math., 8, 703-712, (1960) · Zbl 0098.12104 [33] Kennington, J.; Shalaby, M., An effective subgradient procedure for minimal cost multi-commodity flow problems, Management sci., 23, 994-1004, (1977) · Zbl 0366.90118 [34] Kuhn, H.W.; Tucker, A.W., Nonlinear programming, () · Zbl 0044.05903 [35] Lasdon, L.S., Optimization theory for large systems, (1970), MacMillan New York · Zbl 0224.90038 [36] Lemarech, C., An extension of davidon methods to nondifferentiable problems, (), 95-109 [37] Luenberger, D.G., Introduction to linear and nonlinear programming, (1973), Addison-Wesley Reading, MA · Zbl 0241.90052 [38] Marsten, R.E., The use of the boxstep in discrete optimization, (), 127-144 [39] Marsten, R.E.; Hogan, W.W.; Blankenship, J.W., The boxstep method for large scale optimization, Operations res., 23, 389-405, (1975) · Zbl 0372.90078 [40] Motzkin, R.; Schoenberg, I.J., The relaxation method for linear inequalities, Can. J. math., 6, 393-404, (1954) · Zbl 0055.35002 [41] Muckstadt, J.A.; Koening, S.A., An application of Lagrangian relaxation to scheduling in power generation system, Operations res., 25, 387-403, (1977) · Zbl 0383.90065 [42] Poljak, B.T., A general method of solving extremum problems, Soviet math. dokl., 8, 593-597, (1967) · Zbl 0177.15102 [43] Poljak, B.T., Minimization of unsmooth functionals, U.S.S.R. computational math. and math. phys., 9, 14-29, (1964) · Zbl 0229.65056 [44] Rockafellar, R.T., Duality in nonlinear programming, () · Zbl 0231.90037 [45] Rockafellar, R.T., Convex analysis, (1970), Princeton University Press Princeton, NJ · Zbl 0229.90020 [46] Rosenbrock, H.H., Automatic method for finding the greatest or least value of a function, Comput. J., 3, 175-184, (1960) [47] Shor, N.Z., On the rate of convergence of the generalized gradient method, Kibernetika, 4, (1968) · Zbl 0243.90038 [48] Smeers, Y., An algorithm for some special nondifferentiable optimization problems, Operations res., 25, 808-817, (1977) · Zbl 0385.90093 [49] Tucker, A.W., Least-distance programming, (), 583-588 · Zbl 0208.21703 [50] Wolfe, P., On the convergence of gradient methods under constraint, IBM J. res. develop., 16, 407-411, (1972) · Zbl 0265.90046 [51] Wolfe, P., Algorithm for a least-distance programming problem, (), 190-205 [52] Wolfe, P., A method of conjugate subgradients for minimizing non-differentiable functions, (), 145-173 [53] Zangwill, W.I., Nonlinear programming: A unified approach, (1969), Prentice-Hall Englewood Cliffs, NJ · Zbl 0191.49101 This reference list is based on information provided by the publisher or from digital mathematics libraries. 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