Unconstrained Functional Optimization

This chapter presents how to use the calculus of variations to find the optimum function within a group of functions without considering the constraints. A few examples of functional optimization, including the shortest path and the minimum-time path, are presented. The Matlab implementation of functional optimization is also demonstrated. Figure 4.1 shows possible paths f(x) of a single variable functional between two fixed points \(P_1\) and \(P_2\) . It also shows the optimal function \(f^*(x)\) .