RESOLUTION OF EXTREMISATION PROBLEM USING DUALITY PRINCIPLE
Keywords:
Extremisation problem, Duality Principle, Optimum solution, Hilber space.
Abstract
The use of duality principle for characterizing solution of general optimization problem posed in the Hilbert space was considered. The existence and uniqueness of solution are guaranteed by formulating the minimum problem in a dual space. Furthermore, the solution is shown to be aligned.
References
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Parida, J., Sen, A. 1986. Duality and existence theorem for non-differentiable programming, journal of optimization Theory and Applications, 48(3): 451-458.
Bazaraa, M.S., Sherali, H.D., Shetty, C.M. 1993. Non linear programming (Theory and algorithms) John Wiley, New York.
Rani, O., Kaul, R.N. 1973. Duality theorems for a class of non-convex programming problems, Journal of Optimization Theory and Applications, 11(3): 305-308.
Bamigbola, O.M., Adelodun, J.F., Makanjuola, S.O. 2005. Optimization abstraction in R-Multipliers. A paper submitted to the Journal of Nigerian Mathematical Society (JNMS).
Osinuga, I.A., Bamigbola, O.M. 2004. On global optimization for convex programs on abstract spaces. Journal of the Mathematical Association of Nigeria, 31(2A): 94-98
Ferreira, P.S.G. 1996. The existence and uniqueness of the minimum norm solution to certain linear and nonlinear problems. Signal processing 55(1): 137-139.
Vinter, R.B. 1974. Application of duality theory to a class of composite cost control problems; Journal of Optimization Theory and Applications, 13(4): 436-460.
Lee, Y.-J., Shih, C.-Y. 2002. The Riesz Representation theorem on infinite dimensional spaces and its applications. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 5(1): 41-59.
Aliprants, C.D., Burkishaw, O 1990. Prince of real analysis 92/ed). Academic Press, San Diego.
Kanzow, C., H,Qi., L. Qi 2000. On the minimum norm solution of linear programs. Applied mathematics Report. AMR00/14, 1-2.
Leuenberger, D.G. 1969. Optimization by vector space methods, John Wiley, New York.
Kreyszing, E. 1978. Introductory functional analysis with applications John Wiley, New York.
Clarke, F.H. 1983. Optimization and non-smooth analysis. John Wiley, New York.
Madox, I.J. 1988. Element of functional analysis (2nd ed.). Cambridge University Press, Cambridge.
Parida, J., Sen, A. 1986. Duality and existence theorem for non-differentiable programming, journal of optimization Theory and Applications, 48(3): 451-458.
Bazaraa, M.S., Sherali, H.D., Shetty, C.M. 1993. Non linear programming (Theory and algorithms) John Wiley, New York.
Rani, O., Kaul, R.N. 1973. Duality theorems for a class of non-convex programming problems, Journal of Optimization Theory and Applications, 11(3): 305-308.
Bamigbola, O.M., Adelodun, J.F., Makanjuola, S.O. 2005. Optimization abstraction in R-Multipliers. A paper submitted to the Journal of Nigerian Mathematical Society (JNMS).
Osinuga, I.A., Bamigbola, O.M. 2004. On global optimization for convex programs on abstract spaces. Journal of the Mathematical Association of Nigeria, 31(2A): 94-98
Ferreira, P.S.G. 1996. The existence and uniqueness of the minimum norm solution to certain linear and nonlinear problems. Signal processing 55(1): 137-139.
Vinter, R.B. 1974. Application of duality theory to a class of composite cost control problems; Journal of Optimization Theory and Applications, 13(4): 436-460.
Lee, Y.-J., Shih, C.-Y. 2002. The Riesz Representation theorem on infinite dimensional spaces and its applications. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 5(1): 41-59.
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