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The use of Hestenes’ method of multipliers to resolve dual gaps in engineering system optimization. (English) Zbl 0278.49040
MSC:
49M99Numerical methods in calculus of variations
90C99Mathematical programming
References:
[1]Everett, H., III,Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources, Operations Research, Vol. 11, No. 3, 1963.
[2]Lasdon, L. S.,Optimization Theory for Large Systems, McMillan Publishing Company, New York, New York, 1970.
[3]Greenberg, H. J.,Lagrangian Duality Gaps: Their Source and Resolution, Southern Methodist University, Technical Report No. CP-69005, 1969.
[4]Gould, F. J.,Extensions of Lagrange Multipliers in Nonlinear Programming, SIAM Journal on Applied Mathematics, Vol. 17, No. 6, 1969.
[5]Bellman, R., andKarush, W.,On a New Functional Transform in Analysis: The Maximum Transform, Bulletin of American Mathematical Society, Vol. 67, No. 5, 1961.
[6]Greenberg, H. J., andPierskalla, W. P.,Surrogate Mathematical Programs, Operations Research, Vol. 18, No. 5, 1970.
[7]Glover, F.,A Multiphase-Dual Algorithm for the Zero-One Integer Programming Problem, Operations Research, Vol. 16, No. 4, 1968.
[8]Loane, E. P.,An Algorithm to Solve Finite Separable Constrained Optimization Problems, Operations Research, Vol. 19, No. 6, 1971.
[9]Bellmore, M., Greenberg, H. J., andJarvis, J. J.,Generalized Penalty Function Concepts in Mathematical Optimization, Operations Research, Vol. 18, No. 2, 1970.
[10]Falk, J. E., andSoland, R. M.,An Algorithm for Separable Nonconvex Programming Problems, Management Science, Vol. 15, No. 9, 1969.
[11]Soland, R. M.,An Algorithm for Separable Non-Convex Programming Problems II: Non-Convex Constraints, Management Science, Vol. 17, No. 11, 1971.
[12]Greenberg, H. J.,Bounding Nonconvex Programs by Conjugates, Operations Research, Vol. 21, No. 1, 1973.
[13]McGalliard, R. L., andWesterberg, A. W.,Structural Sensitivity Analysis in Design Synthesis, The Chemical Engineering Journal, Vol. 4, No. 4, 1972.
[14]Rockafellar, R. T.,Non-Linear Programming, American Mathematical Society Summer Seminar on the Mathematics of the Decision Sciences, Stanford University, 1967.
[15]Hestenes, M. R.,Multiplier and Gradient Methods, Journal of Optimization Theory and Applications, Vol. 4, No. 5, 1969.
[16]Miele, A., Moseley, P. E., Levy, A. V., andCoggins, G. M.,On the Method of Multipliers for Mathematical Programming Problems, Journal of Optimization Theory and Applications, Vol. 10, No. 1, 1972.
[17]McGalliard, R. L.,Structural Sensitivity Analysis in Design Synthesis, University of Florida, Ph.D. Thesis, 1971.