Primal Affine Interior Point Method and Dual Affine Interior Point Method

This package contains two interior point method implementations: the Primal Affine Interior Point Method and the Dual Affine Interior Point Method. Both algorithms are designed to solve linear programming problems efficiently using interior point optimization techniques. The Primal Affine method works directly with the original problem formulation, while the Dual Affine method operates on the dual problem representation. Both implementations follow the affine-scaling approach, which uses affine transformations to navigate through the interior of the feasible region toward the optimal solution. Before using these programs, users must provide an initial interior point that satisfies all constraints strictly. The algorithms require this starting point to begin their iterative optimization process. If you don't have a readily available initial interior point, we will provide a separate program that automatically generates valid initial points. This complementary utility will be sent in our next communication. Key implementation features include: - Step-size control using line search methods - Convergence criteria based on duality gap and feasibility tolerance - Matrix operations for solving linear systems at each iteration - Efficient handling of constraint boundaries while maintaining interior points