Penalty function method algorithm

Following is the computational algorithm to solve this problem using the penalty function method ... 

Develop a computational algorithm based on the penalty function method to solve Example 8.4 (p. 254) subject to the following constraints ... 

The performance of the penalty function algorithm is heavily influenced by the value chosen for a.. The larger the value of o. the better the constraints are satisfied but the slower the rate of convergence. Optimizations with very high values of ct,. encounter severe convergence problems. However, the method is very general and... 

Because of the occurrence of ill-conditioning, pure penalty methods have been replaced by more efficient algorithms. In SLP and SQP, a merit function is used within the line search phase of these algorithms. 

The two contaminant plumes are represented in the first stage of the optimization formulation with a set of 110 control points along the plume boundaries. These same control point locations are used as starting points for particles when forward tracking is used in the second stage of the solution process. For the unconfined simulation, additional constraints are included to require a minimum saturated thickness of 1.5 m at each well cell. Both confined and unconfined assumptions are simulated under two sets of penalty parameters. Recall that the solution algorithm uses the penalty method for the plume capture constraints, in which each constraint violation is multiplied by a penalty parameter and added to the objective function. 

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