MATLAB Implementation Using Interior Penalty Function Method

The analysis of optimization case studies can be significantly enhanced by implementing the interior penalty function method through MATLAB programming. This mathematical approach incorporates a penalty term into the objective function to enforce constraint satisfaction, where the penalty term's magnitude can be dynamically adjusted based on constraint importance. The MATLAB implementation typically involves defining a barrier function that grows towards infinity as the solution approaches constraint boundaries, ensuring the algorithm remains within feasible regions. Key MATLAB functions commonly used in this implementation include fmincon for constrained optimization, along with custom penalty function definitions that employ logarithmic or inverse barrier functions. The algorithm workflow generally follows these steps: parameter initialization, penalty coefficient adjustment, iterative optimization using gradient-based methods, and convergence checking based on tolerance thresholds. This method produces more reliable and precise optimization results, leading to improved decision-making in complex scenarios. The interior penalty function method has gained widespread adoption across engineering disciplines, economic modeling, and financial analysis due to its robust handling of constrained optimization problems and flexibility in adapting to various problem structures. MATLAB's computational capabilities further enhance method effectiveness through efficient matrix operations and built-in optimization solvers.