MATLAB Implementation of Constrained Optimization Algorithms

In this article, we explore constrained optimization algorithms, specifically focusing on the Lagrange Multiplier Method. This algorithm is designed to solve optimization problems where one or more variables are subject to certain constraints. We will examine its mathematical foundation and demonstrate how to implement it using MATLAB programming. The implementation typically involves defining the objective function, constraint equations, and solving the resulting system using MATLAB's symbolic toolbox or optimization functions like fmincon. We will also discuss practical applications of this algorithm across various fields such as economics, physics, and engineering. Key implementation aspects include handling equality/inequality constraints, calculating partial derivatives, and iteratively solving the Lagrangian system. Let's delve deeper into this powerful algorithm to better understand its operational principles and real-world applications through practical MATLAB code examples.