Combination of Penalty Function, Lagrange Multiplier and Conjugate Gradient Methods for the Solution of Constrained Optimization Problems

In this paper, we combined Langrage Multiplier, Penalty Function and Conjugate Gradient Methods (CPLCGM), to enable Conjugate Gradient Method (CGM) to be employed for solving constrained optimization problems. In the year past, Langrage Multiplier Method (LMM) has been used extensively to solve constrained optimization problems likewise Penalty Function Method (PFM). 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 it can be properly amended. This, then call for the CPLCGM that is aimed at taking care of some constrained optimization problems, either with equality or inequality constraint but in this paper, we focus on equality constraints. The authors of this paper desired that, with the construction of the new Algorithm, it will circumvent the difficulties undergone using only LMM and as well as PFM 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 and compared the results with the LMM and PFM.