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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
Authors
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
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Abstract
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.
Keywords
Lagrange Multiplier Method, Constrained Optimization Problem, Conjugate Gradient Method, Numerical Experiments of the Lagrange Multiplier Conjugate Gradient Method
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. doi: 10.11648/j.ajam.20140206.15
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