Matches in SemOpenAlex for { <https://semopenalex.org/work/W4387596247> ?p ?o ?g. }
Showing items 1 to 69 of
69
with 100 items per page.
- W4387596247 abstract "The top-$k$-sum operator computes the sum of the largest $k$ components of a given vector. The Euclidean projection onto the top-$k$-sum constraint serves as a crucial subroutine in iterative methods to solve composite superquantile optimization problems. In this paper, we introduce a solver that implements two finite-termination algorithms to compute this projection. Both algorithms have complexity $O(n)$ when applied to a sorted $n$-dimensional input vector, where the absorbed constant is independent of $k$. This stands in contrast to the existing grid-search-inspired method that has $O(k(n-k))$ complexity. The improvement is significant when $k$ is linearly dependent on $n$, which frequently encountered in practical superquantile optimization applications. In instances where the input vector is unsorted, an additional cost is incurred to (partially) sort the vector. To reduce this cost, we further derive a rigorous procedure that leverages approximate sorting to compute the projection, which is particularly useful when solving a sequence of similar projection problems. Numerical results show that our methods solve problems of scale $n=10^7$ and $k=10^4$ within $0.05$ seconds, whereas the existing grid-search-based method and the Gurobi QP solver can take minutes to hours." @default.
- W4387596247 created "2023-10-13" @default.
- W4387596247 creator A5003300933 @default.
- W4387596247 creator A5071987706 @default.
- W4387596247 date "2023-10-11" @default.
- W4387596247 modified "2023-10-14" @default.
- W4387596247 title "On $O(n)$ Algorithms for Projection onto the Top-$k$-sum Constraint" @default.
- W4387596247 doi "https://doi.org/10.48550/arxiv.2310.07224" @default.
- W4387596247 hasPublicationYear "2023" @default.
- W4387596247 type Work @default.
- W4387596247 citedByCount "0" @default.
- W4387596247 crossrefType "posted-content" @default.
- W4387596247 hasAuthorship W4387596247A5003300933 @default.
- W4387596247 hasAuthorship W4387596247A5071987706 @default.
- W4387596247 hasBestOaLocation W43875962471 @default.
- W4387596247 hasConcept C111696304 @default.
- W4387596247 hasConcept C111919701 @default.
- W4387596247 hasConcept C11413529 @default.
- W4387596247 hasConcept C114614502 @default.
- W4387596247 hasConcept C126255220 @default.
- W4387596247 hasConcept C187691185 @default.
- W4387596247 hasConcept C199360897 @default.
- W4387596247 hasConcept C2524010 @default.
- W4387596247 hasConcept C2776036281 @default.
- W4387596247 hasConcept C2777027219 @default.
- W4387596247 hasConcept C2778112365 @default.
- W4387596247 hasConcept C2778770139 @default.
- W4387596247 hasConcept C33923547 @default.
- W4387596247 hasConcept C41008148 @default.
- W4387596247 hasConcept C45354692 @default.
- W4387596247 hasConcept C54355233 @default.
- W4387596247 hasConcept C57493831 @default.
- W4387596247 hasConcept C86803240 @default.
- W4387596247 hasConcept C96147967 @default.
- W4387596247 hasConceptScore W4387596247C111696304 @default.
- W4387596247 hasConceptScore W4387596247C111919701 @default.
- W4387596247 hasConceptScore W4387596247C11413529 @default.
- W4387596247 hasConceptScore W4387596247C114614502 @default.
- W4387596247 hasConceptScore W4387596247C126255220 @default.
- W4387596247 hasConceptScore W4387596247C187691185 @default.
- W4387596247 hasConceptScore W4387596247C199360897 @default.
- W4387596247 hasConceptScore W4387596247C2524010 @default.
- W4387596247 hasConceptScore W4387596247C2776036281 @default.
- W4387596247 hasConceptScore W4387596247C2777027219 @default.
- W4387596247 hasConceptScore W4387596247C2778112365 @default.
- W4387596247 hasConceptScore W4387596247C2778770139 @default.
- W4387596247 hasConceptScore W4387596247C33923547 @default.
- W4387596247 hasConceptScore W4387596247C41008148 @default.
- W4387596247 hasConceptScore W4387596247C45354692 @default.
- W4387596247 hasConceptScore W4387596247C54355233 @default.
- W4387596247 hasConceptScore W4387596247C57493831 @default.
- W4387596247 hasConceptScore W4387596247C86803240 @default.
- W4387596247 hasConceptScore W4387596247C96147967 @default.
- W4387596247 hasLocation W43875962471 @default.
- W4387596247 hasOpenAccess W4387596247 @default.
- W4387596247 hasPrimaryLocation W43875962471 @default.
- W4387596247 hasRelatedWork W1499137908 @default.
- W4387596247 hasRelatedWork W1575541347 @default.
- W4387596247 hasRelatedWork W1650714435 @default.
- W4387596247 hasRelatedWork W2087236959 @default.
- W4387596247 hasRelatedWork W2353465789 @default.
- W4387596247 hasRelatedWork W2366513887 @default.
- W4387596247 hasRelatedWork W2370633508 @default.
- W4387596247 hasRelatedWork W2376660845 @default.
- W4387596247 hasRelatedWork W2386007012 @default.
- W4387596247 hasRelatedWork W2942431073 @default.
- W4387596247 isParatext "false" @default.
- W4387596247 isRetracted "false" @default.
- W4387596247 workType "article" @default.