Volume 27 | Number 1 | Year 2015 | Article Id. IJMTT-V27P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V27P508
A review has been done on the growth and improvement of solution of non linear programming problems under various factors. The mathematical work of Kuhn-Tucker, Fritz John, Mangasarian, Wolfe, Vond, Kanniappan has been traced and compared.
[1] MANGASARIAN AND S. FROMOVITZ ,The Fritz John Necessary Optimality Conditions in the Presence of Equality and Inequality Constraints, journal of mathematical analysis and applications 17, 37-47 (1967)
[2] H. W. KUHN AND A. W. TUCKER. Nonlinear programming. In “Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability” (J. Neyman, ed.), pp. 481-492. Univ. of Calif. Press, Berkeley, Calif., 1951.
[3] F. JOHN. Extremum problems with inequalities as side conditions. In “Studies and Essays, Courant Anniversary Volume” (K. 0. Friedrichs, 0. E. Neugebauer and J. J. Stoker, eds.), pp. 187- 204. Wiley (Interscience), New York, 1948. [4] P. WOLFE, a duality theorem for nonlinear programming, quart. appl. math. 19(1961), 239-244.
[5] MURRAY SCHECHTER,A Subgradient Duality Theorem, journal of mathematical analysis and applications 61, 850-855 (1977)
[6] BERTRAM VOND, A Class of Nondifferentiable Mathematical Programming Problems, Journal of mathematical analysis and applications 46, 169-174 (1974)
[7] SHINJI TANIMOTO, Duality for a Class of Nondifferentiable Mathematical Programming Problems, Journal of mathematical analysis and applications 79, 286-294 (1981)
[8] P.KANNIAPPAN,Nondifferentiable Convex MultiobjectiveProgramming I Journal of optimization theory and applications: vol. 40, no. 2, june 1983
[9] LAI, H. C., and LIu, J. C., Necessary and Sufficient Conditions for Pareto Optimality in Nondifferentiable Convex Multiobjective Programming, NationalTsing Hua University, Taiwan, Prepdnt, 1984.
[10] M1NAMI, M., Weak Pareto Optimality of Muhiobjective Problems in a Locally Convex Linear Topological Space, Journal of Optimization Theory and Applications, Vol. 34, pp. 469-484, 1981.
[11] TANINO, T., and SAWARAKI, Y., Duality Theory in Multiobjective Programming, Journal of Optimization Theory on Sub gradient Duality, Journal of Mathematical Analysis and Applications, Vol. 71, pp. 251-262, 1979.
[12] . ROCKAFELLAR, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.nd Applications, Vol. 27, pp. 509-529, 1979.
Rashi Khubnani,Tarunika Sharma, "A note on mathematical programming problems," International Journal of Mathematics Trends and Technology (IJMTT), vol. 27, no. 1, pp. 38-40, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V27P508