Controlled Optimization of Quadratic Functions in ℝⁿ

2025/08/21 by Jean-Jacques Godeme, Godeme, Jean-Jacques
Computer Science · #FOS: Mathematics #Numerical Methods and Algorithms #Optimization and Control (math.OC) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2508.15515

openalex publication_date 2025/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we introduce and study the controllability of the trajectories of a linear dynamical system, which can be used to solve the minimization of a quadratic function in finite dimension. We named this dynamical system the controlled quadratic gradient flow. Finally, we introduce what we call the controlled quadratic gradient descent and the controlled proximity operator which are respectively the Euler explicit and implicit discretization of the controlled gradient flow.

Citations

• From the Ravine method to the Nesterov method and vice versa: a dynamical system perspective
• Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information
• Convergence of the newton process to multiple solutions

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