zbMATH — the first resource for mathematics

A finite steepest-ascent algorithm for maximizing piecewise-linear concave functions. (English) Zbl 0362.90114

90C30 Nonlinear programming
Full Text: DOI
[1] Demyanov, V. F.,Algorithms for Some Minimax Problems, Journal of Computer and Systems Sciences, Vol. 2, pp. 342-380, 1968. · Zbl 0177.23104
[2] Bazaraa, M. S., andGoode, J. J.,A Survey of Various Tactics for Generating Lagrangian Multipliers in the Context of Lagrangian Duality, Georgia Institute of Technology, School of Industrial and Systems Engineering, Working Paper, 1974. · Zbl 0405.90062
[3] Fisher, M. L., Northup, W. D., andShapiro, J. F.,Using Duality to Solve Discrete Optimization Problems: Theory and Computational Experience, Mathematical Programming Study, Vol. 3, pp. 56-94, 1975. · Zbl 0367.90087
[4] Lasdon, L. S.,Optimization Theory for Large Systems, The MacMillan Company, New York, New York, 1970. · Zbl 0224.90038
[5] Geoffrion, A. M.,Elements of Large Scale Mathematical Programming, Parts I and II, Management Science, Vol. 16, pp. 652-691, 1970. · Zbl 0209.22801
[6] Wolfe, P.,Algorithm for a Least Distance Programming Problem, Mathematical Programming Study, Vol. 3, pp. 145-173, 1975.
[7] Grinold, R. C.,Steepest Ascent for Large Scale Linear Programs, SIAM Review, Vol. 14, pp. 447-464, 1972. · Zbl 0281.90044
[8] Dantzig, G. B., andWolfe, P.,The Decomposition Algorithm for Linear Programming, Econometrica, Vol. 29, pp. 767-778, 1961. · Zbl 0104.14305
[9] Brooks, R., andGeoffrion, A. M.,Finding Everett’s Lagrange Multipliers by Linear Programming, Operations Research, Vol. 14, pp. 1149-1153, 1966.
[10] Held, M., Wolfe, P., andGrowder, H. D.,Validation of Subgradient Optimization, Mathematical Programming, Vol. 6, pp. 62-88, 1974. · Zbl 0284.90057
[11] Eaves, C. B.,Solving Piecewise Linear Convex Equations, Mathematical Programming Study, Vol. 1, pp. 96-119, 1974. · Zbl 0356.15003
[12] Eaves, C. B., andScarf, H.,The Solution of Systems of Piecewise Linear Equations, Mathematics of Operations Research, Vol. 1, pp. 1-31, 1976. · Zbl 0458.65056
[13] Tucker, A. W.,Least-Distance Programming, Proceedings of the Princeton Symposium on Mathematical Programming, Edited by H. W. Kuhn, Princeton University Press, Princeton, New Jersey, 1971.
[14] Bazaraa, M. S., Goode, J. J., andRardin, R. L.,An Algorithm for Finding the Shortest Element of a Polyhedral Set with Applications to Lagrangian Duality, Journal of Mathematical Analysis and Applications (to appear). · Zbl 0383.90073
[15] Luenberger, D. G.,Optimization by Vector Space Methods, The MacMillan Company, New York, New York, 1969. · Zbl 0176.12701
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.