MATLAB Implementation of Interior Point Method
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We present a programming-based approach using the Interior Point Method to compute optimal solutions. This optimization technique allows for more efficient problem-solving through barrier functions that handle inequality constraints by keeping iterations within the feasible region. Our implementation includes a complete MATLAB program featuring key algorithmic components: a Newton-Raphson iteration solver for the Karush-Kuhn-Tucker conditions, logarithmic barrier functions for constraint handling, and adaptive step-size control for convergence. The accompanying technical documentation explains the implementation methodology, including the primal-dual formulation, centrality parameters adjustment, and termination criteria based on duality gap tolerance. This comprehensive package serves as an essential tool for solving constrained optimization problems, providing both theoretical understanding and practical implementation guidelines.
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