Optimization problems and techniquesContinuous optimization versus discrete optimization, Unrestricted optimization versus restricted optimization, none, one or many objectives, Deterministic optimization versus stochastic optimization. Optimization methods seek to find variable values that optimize a multivariate objective function under a set of constraints. Restrictions define a search space, also known as a feasible region, within which the solution must be included. Among optimization methods (Luenberger, 200), linear programming is widely used because of its ease of implementation and its greater stability and convergence compared to other methods (for example, the methods use a single search point and their search begins with a good initial estimate of the search point).
Optimization methods are used in many areas of study to find solutions that maximize or minimize some parameters of the study, such as minimizing costs in the production of a good or service, maximizing profits, minimizing raw material in the development of a good, or maximizing production. In the case of large-scale problems, such as the allocation of resources on a global scale, various techniques have been developed based on exact or heuristic methods. In addition, the optimal solution provided by the RO method is optimal for all interpretations of the uncertain parameter, since the worst-case scenario is taken into account in the decision-making process. The purpose of this chapter is to briefly analyze iterative numerical methods based on the gradient descent algorithm to optimize an unrestricted nonlinear problem in order to design an FNN.
In general, it is difficult to obtain a realistic PDF of uncertain parameters; however, the most advanced RO method is capable of solving energy system problems with a number of uncertainties.