HilbertSpace Convex Optimization Utilizing Parallel Reduction of Linear Inequality to Equality Constraints
Abstract
We present a parallel optimization algorithm for a convex function $f$ on a Hilbert Space, $\mathbb H$, under $r \in \mathbb N$ linear inequality constraints by finding optimal points over sets of equality constraints. Given enough threads, and strict convexity, the complexity is $O(r \langle \cdot, \cdot\rangle$ min$_{\mathbb H} f)$. The method works on constrained spaces with empty interiors, furthermore no feasible point is required, and the algorithm recognizes when the feasible space is empty.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.07565
 Bibcode:
 2021arXiv210907565D
 Keywords:

 Mathematics  Optimization and Control