2020/03/31 by Simon Foucart, Foucart, Simon
Engineering · Mathematics · #41A65 #46N10 #49M29 #65K05 #90C22 #90C47 #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Markov Chains and Monte Carlo Methods #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2004.00195
openalex publication_date 2020/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Models based on approximation capabilities have recently been studied in the\ncontext of Optimal Recovery. These models, however, are not compatible with\noverparametrization, since model- and data-consistent functions could then be\nunbounded. This drawback motivates the introduction of refined approximability\nmodels featuring an added boundedness condition. Thus, two new models are\nproposed in this article: one where the boundedness applies to the target\nfunctions (first type) and one where the boundedness applies to the\napproximants (second type). For both types of model, optimal maps for the\nrecovery of linear functionals are first described on an abstract level before\ntheir efficient constructions are addressed. By exploiting techniques from\nsemidefinite programming, these constructions are explicitly carried out on a\ncommon example involving polynomial subspaces of \C[-1,1].\n