# A generalized projection-based scheme for solving convex constrained optimization problems

arXiv: https://arxiv.org/abs/1803.05617 · HTML: https://mlsanity.com/paper/1803.05617/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2018.

## Built on by (most cited first, 1 of 1)

- [Differentiable Projection for Constrained Deep Learning](https://mlsanity.com/paper/2111.10785/) (2021)

## Abstract (arXiv)

In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility problems by iteratively constraining the objective function from above until the feasibility problem is inconsistent. For each of the feasibility problems one may apply any of the existing projection methods for solving it. In particular, the scheme allows the use of subgradient projections and does not require exact projections onto the constraints sets as in existing similar methods. We also apply the newly introduced concept of superiorization to optimization formulation and compare its performance to our scheme. We provide some numerical results for convex quadratic test problems as well as for real-life optimization problems coming from medical treatment planning.