A smoothed augmented Lagrangian framework for nonsmooth convex optimization

Thu, 18 Aug 2022 01:00:00 +0000

We focus on developing an Augmented Lagrangian Method (ALM) frame- work for resolving nonsmooth convex optimization problems. The problem of interest is formulated as follows.

$\min_{\mathbf{x}\in\mathcal{X}} f(\mathbf{x}) \quad \text{subject to} \quad g(\mathbf{x}) \leq 0$

where $f$ and $g$ are nonsmooth convex functions and $\mathcal{X}\subset \mathbb{R}^n$ is closed and convex.

The presence of nonsmoothness introduces additional challenges to the solution methods. However, by leveraging smoothing techniques, we are able to propose a comprehensive ALM framework that can contend with nonsmoothness.

Opioid Misuse Classification

Tue, 27 Apr 2021 00:00:00 +0000

In this project, we constructed several machine learning models combing with oversampling techniques for a better prediction of opioid mises for all age groups. In addition, we see the great potential of these techniques applied to a more general imbalanced data problem.

In the main modeling procedure, we fitted six Machine Learning (ML) prediction models of opioid misuse using three strategies.

Use standard ML algorithms include Logistic regression, penalized Logistic regression, Decision Tree, Random Forests, and Multilayer Perceptron.
The same standard ML methods are adopted, followed by the oversampling procedure.
Employ special ML models, RUSBoost and Relogit for this imbalanced classification problem.

When evaluating the models’ performance, 10-fold stratified cross validation was implemented and AUC was chosen for the evaluation metric.

The results showed when implementing the standard ML algorithms without oversampling, the penalized logistic regression performed slightly better. Besides, RUSBoost and Relogit, special ML models for the imbalanced classification, improve the predictive models’ performance. This proved that RUSBoost (0.697) and Relogit (0.724) are more effective for the imbalanced data set.

However, after oversampling, RUSBoost and Relogit do not show a great improvement in predictive ability. All other standard ML models significantly enhanced predictive ability, especially Random Forest (0.997) and Decision Tree (0.977).

Projects | Peixuan Zhang

A smoothed augmented Lagrangian framework for nonsmooth convex optimization

Opioid Misuse Classification