# Hilbert-Space Convex Optimization Utilizing Parallel Reduction of Linear Inequality to Equality Constraints

@inproceedings{Neimand2021HilbertSpaceCO, title={Hilbert-Space Convex Optimization Utilizing Parallel Reduction of Linear Inequality to Equality Constraints}, author={Ephraim Neimand and Serban Sabau}, year={2021} }

We present a parallel optimization algorithm for a convex function f on a Hilbert space, H, under r ∈ N linear inequality constraints by finding optimal points over sets of equality constraints. Let ν(⋅) be the time complexity of some process, then given enough threads, and strict convexity, the complexity of our algorithm is O(r ⋅ ν(⟨⋅, ⋅⟩) ⋅ ν(minH f)). The method works on constrained spaces with empty interiors, furthermore no feasible point is required, and the algorithm recognizes when the… Expand

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