A new perspective on parameter study of optimization problems

TL;DR

This paper introduces a novel approach combining sensitivity analysis and differential equations to quantify how uncertain parameters affect the solutions of optimization problems, demonstrated through analytic and PDE-based examples.

Contribution

It presents a new perspective that integrates sensitivity analysis and ODEs for parameter uncertainty quantification in optimization problems.

Findings

Effective quantification of parameter uncertainty impacts on minimizers.

Application to inverse problems governed by PDEs.

Illustrative examples demonstrating the approach's utility.

Abstract

We provide a new perspective on the study of parameterized optimization problems. Our approach combines methods for post-optimal sensitivity analysis and ordinary differential equations to quantify the uncertainty in the minimizer due to uncertain parameters in the optimization problem. We illustrate the proposed approach with a simple analytic example and an inverse problem governed by an advection diffusion equation.