# Efficient DC Algorithm for Constrained Sparse Optimization

arXiv: https://arxiv.org/abs/1701.08498 · HTML: https://mlsanity.com/paper/1701.08498/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2017.

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## Abstract (arXiv)

We address the minimization of a smooth objective function under an ℓ0-constraint and simple convex constraints. When the problem has no constraints except the ℓ0-constraint, some efficient algorithms are available; for example, Proximal DC (Difference of Convex functions) Algorithm (PDCA) repeatedly evaluates closed-form solutions of convex subproblems, leading to a stationary point of the ℓ0-constrained problem. However, when the problem has additional convex constraints, they become inefficient because it is difficult to obtain closed-form solutions of the associated subproblems. In this paper, we reformulate the problem by employing a new DC representation of the ℓ0-constraint, so that PDCA can retain the efficiency by reducing its subproblems to the projection operation onto a convex set. Moreover, inspired by the Nesterov's acceleration technique for proximal methods, we propose the Accelerated PDCA (APDCA), which attains the optimal convergence rate if applied to convex programs, and performs well in numerical experiments.