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Projection and restriction methods in geometric programming and related problems. (English) Zbl 0369.90115

MSC:
90C30 Nonlinear programming
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[1] Duffin, R. J., Peterson, E. L., andZener, C.,Geometric Programming?Theory and Applications, John Wiley and Sons, New York, New York, 1967. · Zbl 0171.17601
[2] Abrams, R.,Consistency, Superconsistency and Dual Degeneracy in Geometric Programming, Operations Research, Vol. 24, pp. 325-335, 1976. · Zbl 0348.90119 · doi:10.1287/opre.24.2.325
[3] Williams, A. C.,Complementary Theorems for Linear Programming, SIAM Review, Vol. 12, pp. 135-137, 1970. · Zbl 0193.18606 · doi:10.1137/1012015
[4] Shefi, A.,Reduction of Linear Inequality Constraints and Determination of All Feasible Extreme Points, Stanford University, PhD Dissertation, 1969.
[5] Luenberger, D. G.,Introduction to Linear and Nonlinear Programming, Addison-Wesley Publishing Company, Reading, Massachusetts, 1973. · Zbl 0297.90044
[6] Rockafellar, R. T.,Convex Functions and Dual Extremum Problems, Harvard University, PhD Dissertation, 1963.
[7] Peterson, E. L.,Fenchel’s Hypothesis and the Existence of Recession Directions in Convex Programming, Northwestern University, Center for Mathematical Studies in Economics and Management Science, Discussion Paper No. 152, 1976.
[8] Wu, C. T.,Reduction and Restriction Methods for Simplifying and Solving Nonlinear Programming Problems, Northwestern University, PhD Dissertation, 1975.
[9] Abrams, R.,Projections of Convex Programs with Unattained Infima, SIAM Journal on Control, Vol. 13, pp. 706-718, 1975. · Zbl 0297.90071 · doi:10.1137/0313040
[10] Peterson, E. L., andEcker, J. G.,Geometric Programming: Duality in Quadratic Programming and Lp-Approximation, III, Degenerate Programs, Journal of Mathematical Analysis and Applications, Vol. 24, pp. 365-383, 1970. · Zbl 0183.49003 · doi:10.1016/0022-247X(70)90085-5
[11] Abrams, R.,Degenerate Quadratic Programming and Lp-Approximation Problems, Journal of Mathematical Analysis and Applications, Vol. 55, No. 2, 1976. · Zbl 0372.90105
[12] Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1969. · Zbl 0186.23901
[13] Stoer, J., andWitzgall, C.,Convexity and Optimization in Finite Dimensions, I, Springer-Verlag, New York, New York, 1970. · Zbl 0203.52203
[14] Peterson, E. L.,Symmetric Duality for Generalized Unconstrained Geometric Programming, SIAM Journal of Applied Mathematics, Vol. 19, pp. 487-526, 1970. · Zbl 0205.48001 · doi:10.1137/0119049
[15] Abrams, R. A., andKerzner, L.,A Simplified Test for Optimality, Journal of Optimization Theory and Applications (to appear).
[16] Magnanti, T. L.,Fenchel and Lagrange Duality Are Equivalent, Mathematical Programming, Vol. 7, pp. 253-258, 1974. · Zbl 0296.90037 · doi:10.1007/BF01585523
[17] Ben-Tal, A., Ben-Israel, A., andZlobec, S.,Characterization of Optimality in Convex Programming Without a Constraint Qualification, Journal of Optimization Theory and Applications, Vol. 20, pp. 417-437, 1976. · Zbl 0327.90025 · doi:10.1007/BF00933129
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