A Function Approximation Approach for Parametric Optimization
提出一种新方法，通过将一阶最优性条件转化为方程，并用函数逼近原问题和对偶问题的解，将参数优化问题简化为单个非线性最小二乘问题，适用于需要快速评估参数变化下最优解的场景。
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.