Understanding Penalty Function To Unconstrained Optimization Problem:- Kalu Wisdom N

ABSTRACT viii This work examines the application ofthe Exterior Penalty Method in solving constrained optimization problems by transforming them into equivalent unconstrained optimization problems. The method incorporates a penalty term into the objective function, imposing a cost whenever the constraints are violated. As the penalty parameter is progressively increased, the unconstrained solution converges to the optimal solution ofthe original constrained problem. The study focuses on the quadratic exterior penalty function and demonstrates its implementation on optimization problems involving both equality and inequality constraints. Analytical techniques, including partial differentiation and the solution ofsimultaneous equations, are employed to obtain the optimum values. Numerical examples are presented to illustrate the effectiveness and convergence ofthe method. The results show that the Exterior Penalty Method provides a systematic and efficient approach for solving constrained optimization problems through a sequence of unconstrained optimization problems, making it a valuable technique in mathematical optimization and engineering applications