# A lagrange programming neural network approach for nuclear norm optimization

## TL;DR

This paper introduces a new neural network method for optimizing the nuclear norm, showing better performance in image recovery.

## Contribution

A novel Lagrangian programming neural network is proposed for nuclear norm minimization with proven convergence.

## Key findings

- The proposed LPNN outperforms traditional algorithms in image recovery tasks.
- Convergence conditions of LPNN are established using the Lyapunov method.
- Experiments confirm the convergence and effectiveness of the LPNN approach.

## Abstract

This article proposes a continuous-time optimization approch instead of tranditional optimiztion methods to address the nuclear norm minimization (NNM) problem. Refomulating the NNM into a matrix form, we propose a Lagrangian programming neural network (LPNN) to solve the NNM. Moreover, the convergence condtions of LPNN are presented by the Lyapunov method. Convergence experiments are presented to demonstrate the convergence of LPNN. Compared with tranditional algorithms of NNM, the proposed algorithm outperforms in terms of image recovery.