# Some Stability Properties of Parametric Quadratically Constrained Nonconvex Quadratic Programs in Hilbert Spaces

## TL;DR

This paper investigates the stability of solutions and optimal values in nonconvex quadratic programming problems with convex quadratic constraints in Hilbert spaces, focusing on how small data perturbations affect these properties.

## Contribution

It presents new stability properties of the global solution map and the continuity of the optimal value function for such problems.

## Key findings

- Global solution map exhibits stability under small perturbations.
- Optimal value function remains continuous with data changes.
- Results extend stability analysis to infinite-dimensional Hilbert spaces.

## Abstract

Stability of nonconvex quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces is investigated. We present several stability properties of the global solution map, and the continuity of the optimal value function, assuming that the problem data undergoes small perturbations.