A Function Approximation Approach for Parametric Optimization

Abstract

We present a novel approach for approximating the primal and dual parameter-dependent solution functions of parametric optimization problems. We start with an equation reformulation of the first-order necessary optimality conditions. Then, we replace the primal and dual solutions with some approximating functions and find for some test parameters optimal coefficients as solution of a single nonlinear least-squares problem. Under mild assumptions it can be shown that stationary points are global minima and that the function approximations interpolate the solution functions at all test parameters. Further, we have a cheap function evaluation criterion to estimate the approximation error. Finally, we present some preliminary numerical results showing the viability of our approach.

A novel method for studying the wind speed probability distribution and estimating the average wind energy density

“…Currently, there are two types of parameter optimization methods. One is numerical solution methods [28], such as the Lagrange multiplier method and the least squares method etc. The other is bio-inspired optimization algorithm, such as particle swarm algorithm and snake optimizer etc The following section describes the nonlinear least square and snake optimizer, and investigates their advantages and disadvantages through simulation.…”