Solving Constrained Nonlinear Optimization Problems Using fmincon

This article demonstrates how to solve constrained nonlinear optimization problems using MATLAB's fmincon function from the Optimization Toolbox. We begin with an overview of nonlinear optimization concepts and practical applications. The core section provides a comprehensive walkthrough of fmincon implementation, including problem formulation techniques, constraint handling methods, and parameter configuration strategies. Detailed code examples showcase key aspects: defining objective functions using function handles, specifying linear/nonlinear constraints through dedicated constraint functions, setting optimization options via optimoptions, and interpreting output structures containing convergence metrics. We analyze optimization results by examining exit flags, iteration histories, and Lagrange multipliers to validate solution quality. The article concludes with practical applications to real-world engineering problems, supplemented with troubleshooting tips for common convergence issues and performance optimization techniques for large-scale problems. The implementation leverages fmincon's interior-point algorithm for efficient constraint handling while maintaining numerical stability throughout the optimization process.