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.

Reference:

• De Marchi, A., Dreves, A., Gerdts, M., Gottschalk, S., Rogovs, S.: A Function Approximation Approach for Parametric Optimization. J Optim Theory Appl 196, 56–77 (2023). DOI 10.1007/s10957-022-02138-4