Gradient Projection Method with Constraints

Practical testing demonstrates that the MATLAB implementation of the gradient projection method with constraints performs effectively when solving specific optimization problems. This program proves particularly useful for optimization scenarios requiring parameter restrictions within predefined ranges. For instance, during cost minimization processes where certain factors must not exceed specified boundaries, this implementation effectively constrains these parameters within their allowable ranges to achieve optimal solutions. The algorithm works by projecting the gradient direction onto the feasible set at each iteration, ensuring constraint satisfaction while maintaining convergence toward the optimum. Key MATLAB functions involved may include projection operations onto constraint sets and gradient descent steps with feasible direction checks. This program can significantly contribute to practical engineering applications by improving computational efficiency and solution reliability.