Constrained Minimization Solver Function fmincon

In MATLAB, when addressing multidimensional constrained optimization problems, you can utilize the fmincon function. As part of MATLAB's Optimization Toolbox, fmincon specializes in solving constrained minimization problems. This function operates by defining constraint conditions to establish feasible solution spaces while requiring specification of an objective function to determine the minimum value. The algorithm typically employs sequential quadratic programming (SQP) or interior-point methods to iteratively converge toward optimal solutions. Implementation involves key parameters including initial point selection, constraint definitions (linear/nonlinear inequalities/equalities), and optimization options through optimset configurations. Through multiple iterations that evaluate objective functions and constraint violations, fmincon efficiently locates local minima while respecting boundary conditions and nonlinear constraints. Ultimately, fmincon serves as a powerful and flexible tool for solving complex multidimensional constrained optimization challenges in engineering and scientific applications.