Application Of Neural Network To Constrained Optimization Problems Using Penalty Function Approach
ABSTRACT
In this research
work we propose a feed forward neural network for solving constrained
optimization problems with inequality and equality constraints. We employ
penalty functions that transformed a constrained problem into a single
unconstrained problem. The constraints are placed into the objective function
via a penalty parameter in such a way that penalizes any violation of the
constraints. The penalty function constructed is actually an energy function
for the neural network. Assuming differentiability, a local minimum of the
penalty function is found by using a dynamic gradient scheme which provides a
system of differential equations for the input neurons corresponding to the
variables of the given optimization problem. These can then be solved to give
solutions which converge ultimately to the optimal solution of the constrained
optimization problem. We discovered that our approach is easier and fast and
reduces the vigorous steps and assumptions in other methods. Mathcad 14 was
used in executing the program.`
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ANOKWUTE, R (2023). Application Of Neural Network To Constrained Optimization Problems Using Penalty Function Approach. Repository.mouau.edu.ng: Retrieved Dec 04, 2024, from https://repository.mouau.edu.ng/work/view/application-of-neural-network-to-constrained-optimization-problems-using-penalty-function-approach-7-2
ROPHINA, ANOKWUTE. "Application Of Neural Network To Constrained Optimization Problems Using Penalty Function Approach" Repository.mouau.edu.ng. Repository.mouau.edu.ng, 21 Feb. 2023, https://repository.mouau.edu.ng/work/view/application-of-neural-network-to-constrained-optimization-problems-using-penalty-function-approach-7-2. Accessed 04 Dec. 2024.
ROPHINA, ANOKWUTE. "Application Of Neural Network To Constrained Optimization Problems Using Penalty Function Approach". Repository.mouau.edu.ng, Repository.mouau.edu.ng, 21 Feb. 2023. Web. 04 Dec. 2024. < https://repository.mouau.edu.ng/work/view/application-of-neural-network-to-constrained-optimization-problems-using-penalty-function-approach-7-2 >.
ROPHINA, ANOKWUTE. "Application Of Neural Network To Constrained Optimization Problems Using Penalty Function Approach" Repository.mouau.edu.ng (2023). Accessed 04 Dec. 2024. https://repository.mouau.edu.ng/work/view/application-of-neural-network-to-constrained-optimization-problems-using-penalty-function-approach-7-2