2020/04/07 by Warren Hare, Hare, Warren, Gabriel Jarry–Bolduc +1 · 2 citations
Decision Sciences · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Water Systems and Optimization
paper · pdf · doi:10.48550/arxiv.2004.03507
openalex publication_date 2020/04/07 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28
Originally developed in 1954, positive bases and positive spanning sets have\nbeen found to be a valuable concept in derivative-free optimization (DFO). The\nquality of a positive basis (or positive spanning set) can be quantified via\nthe em cosine measure and convergence properties of certain DFO algorithms\nare intimately linked to the value of this measure. However, it is unclear how\nto compute the cosine measure for a positive basis from the definition. In this\npaper, a deterministic algorithm to compute the cosine measure of any positive\nbasis or finite positive spanning set is provided. The algorithm is proven to\nreturn the exact value of the cosine measure in finite time.\n