Optimization is the key component of the AI/ML algorithm. Whatever objective function is proposed, the final step is to optimize it. Convex optimization problems, either unconstrained or constrained, are well explored (see here). Even though, the efficiency or performance still largely depends on the shape of the surface of the objective function. For convex problems, the solution could be trapped at saddle points; or for local convex objective functions, the solution might reach to the local optima instead of global optima. Of course, trying different initial values of parameters is one way to bypass this issue. Here, we introduce another way to find the optima via Monte Carlo simulation, which technically has chance to reach the global optima at any intial points.
The pdf file is available at here.
The corresponding slides is available at here.