Numerical Experiments with the Lagrange Multiplier and Conjugate Gradient Methods (ILMCGM)
American Journal of Applied Mathematics
Volume 2, Issue 6, December 2014, Pages: 221-226
Received: Dec. 21, 2014;
Accepted: Dec. 25, 2014;
Published: Jan. 6, 2015
Views 3043 Downloads 295
Samson Adebayo Olorunsola, Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria
Temitayo Emmanuel Olaosebikan, Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria
Kayode James Adebayo, Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria
Follow on us
In this paper, we imbed Langrage Multiplier Method (LMM) in Conjugate Gradient Method (CGM), which enables Conjugate Gradient Method (CGM) to be employed for solving constrained optimization problems of either equality, inequality constraint or both. In the past, Langrage Multiplier Method has been used extensively to solve constrained optimization problems. However, with some special features in CGM which makes it unique in solving unconstrained optimization problems, we see that this features we be advantageous to solve constrained optimization problems if we can add or subtract one or two things into the CGM. This, then call for the Numerical Experiments with the Lagrange Multiplier Conjugate Gradient Method (ILMCGM) that is aimed at taking care of any constrained optimization problems, either with equality or inequality constraint The authors of this paper desire that, with the construction of the Algorithm, one will circumvent the difficulties undergone using only LMM to solve constrained optimization problems and its application will further improve the result of the Conjugate Gradient Method in solving this class of optimization problem. We applied the new algorithm to some constrained optimization problems of two, three and four variables in which some of the problems are pertain to quadratic functions. Some of these functions are subject to linear, nonlinear, equality and inequality constraints.
Lagrange Multiplier Method, Constrained Optimization Problem, Conjugate Gradient Method, Numerical Experiments of the Lagrange Multiplier Conjugate Gradient Method
To cite this article
Samson Adebayo Olorunsola,
Temitayo Emmanuel Olaosebikan,
Kayode James Adebayo,
Numerical Experiments with the Lagrange Multiplier and Conjugate Gradient Methods (ILMCGM), American Journal of Applied Mathematics.
Vol. 2, No. 6,
2014, pp. 221-226.
RAO, S. S., (1978), Optimization Theory and Applications, Willy and Sons.
THOMAS, F.E., and DAVID, M.H., (2001), Optimization of Chemical Processes, McGraw Hill
IGOR, G., STEPHEN, G. N. and ARIELA, S., (2009), Linear and Nonlinear Optimization, George Mason University, Fairfax, Virginia, SIAM, Philadelphia.
David, G. Hull, (2003), Optimal Control Theory for Applications, Mechanical Engineering Series, Springer-Verlag, New York, Inc., 175 Fifth Avenue, New York, NY 10010.
Bersekas, D. P, (1982), Constrained Optimization and Lagrange Multipliers Method, Academic Press, Inc.
Rockafellar, R. T., (2005), Multiplier Method of Hestenes and Powell applied to convex Programming, Journal of Optimization Theory and Applications, Vol. 4, No. 4.
Triphath S. S and Narenda K. S, (1972), Constrained Optimization Problems Using Multiplier Methods, Journal of Optimization Theory and Applications: Vol. 9, No. 1.