# A new perspective on parameter study of optimization problems

@article{Alexanderian2022ANP, title={A new perspective on parameter study of optimization problems}, author={Alen Alexanderian and Joseph L. Hart and Mason Stevens}, journal={ArXiv}, year={2022}, volume={abs/2209.11580} }

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.

## References

SHOWING 1-10 OF 16 REFERENCES

### HYPERDIFFERENTIAL SENSITIVITY ANALYSIS OF UNCERTAIN PARAMETERS IN PDE-CONSTRAINED OPTIMIZATION

- Computer ScienceInternational Journal for Uncertainty Quantification
- 2020

This article introduces "hyper-differential sensitivity analysis", a goal-oriented analysis which considers the sensitivity of the solution of a PDE-constrained optimization problem to uncertain parameters and formally defines hyper- differential sensitivity indices.

### Sensitivity analysis for nonlinear programming using penalty methods

- MathematicsMath. Program.
- 1976

A theoretical basis is established for utilizing a penalty-function method to estimate sensitivity information of a localsolution and its associated Lagrange multipliers of a large class of nonlinear programming problems with respect to a general parametric variation in the problem functions.

### Optimization Problems with Perturbations: A Guided Tour

- MathematicsSIAM Rev.
- 1998

The emphasis on methods based on upper and lower estimates of the objective function of the perturbed problems allow one to compute expansions of the optimal value function and approximate optimal solutions in situations where the set of Lagrange multipliers is not a singleton, may be unbounded, or is even empty.

### Parametric sensitivity analysis in optimal control of a reaction-diffusion system – part II: practical methods and examples

- MathematicsOptim. Methods Softw.
- 2004

This article devise a practical algorithm that is capable of solving both the unperturbed optimal control problem and the parametric sensitivity problem and provides a second-order expansion of the minimum value function and compares it to the objective values at true perturbed solutions.

### Directional derivatives of optimal solutions in smooth nonlinear programming

- Mathematics
- 1992

We consider a smooth nonlinear program subject to perturbations in the right-hand side of the constraints. We do not assume that the unique solution of the original problem satisfies any…

### Hyper-differential sensitivity analysis for inverse problems constrained by partial differential equations

- MathematicsInverse Problems
- 2020

High fidelity models used in many science and engineering applications couple multiple physical states and parameters. Inverse problems arise when a model parameter cannot be determined directly, but…

### Parametric Sensitivity Analysis in Optimal Control of a Reaction Diffusion System. I. Solution Differentiability

- Mathematics
- 2004

Abstract In this paper we consider a control-constrained optimal control problem governed by a system of semilinear parabolic reaction–diffusion equations. The optimal solutions are subject to…

### Perspectives in flow control and optimization

- Engineering
- 1987

From the Publisher:
Flow control and optimization has been an important part of experimental flow science throughout the last century. As research in computational fluid dynamics (CFD) matured,…

### Randomized algorithms for generalized singular value decomposition with application to sensitivity analysis

- Computer ScienceNumer. Linear Algebra Appl.
- 2021

New randomized algorithms for computing the GSVD which use randomized subspace iteration and weighted QR factorization are proposed, motivated by applications in hyper‐differential sensitivity analysis (HDSA).