Interior Point Method Based on Dual Affine Theory

In engineering applications, the interior point method serves as a fundamental classical algorithm. This MATLAB-developed implementation utilizes the interior point method based on dual affine theory, which operates by searching within the feasible region of the objective function to identify optimal solutions. The algorithm's key advantage lies in its effective handling of complex optimization problems including linear programming, quadratic programming, and semidefinite programming. The MATLAB implementation employs iterative computations that maintain interior points within the feasible region while progressively approaching optimality through affine scaling transformations. The dual affine theory-based approach particularly enhances the algorithm's capability to manage inequality constraints more effectively, making it exceptionally suitable for broad engineering applications. The code structure typically involves initialization of interior points, iterative updates using affine scaling matrices, and convergence checks using duality gap calculations. This implementation provides greater flexibility and reliability in engineering design by offering robust constraint handling and systematic optimization progression through barrier parameter adjustments and Newton step computations.