# Level-set methods for convex optimization

arXiv: https://arxiv.org/abs/1602.01506 · HTML: https://mlsanity.com/paper/1602.01506/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2016.

## Built on by (most cited first, 5 of 5)

- [A Retention-Centric Framework for Continual Learning with Guaranteed Model Developmental Safety](https://mlsanity.com/paper/2410.03955/) (2024)
- [Projection-Free Functional Constrained Optimization for Risk Aversion and Sparsity Control](https://mlsanity.com/paper/2210.05108/) (2022)
- [Gauges and Accelerated Optimization over Smooth and/or Strongly Convex Sets](https://mlsanity.com/paper/2303.05037/) (2023)
- [l1-Norm Minimization with Regula Falsi Type Root Finding Methods](https://mlsanity.com/paper/2105.00244/) (2021)
- [First-order methods for Stochastic Variational Inequality problems with Function Constraints](https://mlsanity.com/paper/2304.04778/) (2023)

## Abstract (arXiv)

Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the roles of the objective and constraint functions, and instead approximately solves a sequence of parametric level-set problems. A zero-finding procedure, based on inexact function evaluations and possibly inexact derivative information, leads to an efficient solution scheme for the original problem. We describe the theoretical and practical properties of this approach for a broad range of problems, including low-rank semidefinite optimization, sparse optimization, and generalized linear models for inference.