FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4313591350> ?p ?o ?g. }

• W4313591350 abstract "We propose and analyze a new dynamical system with a closed-loop control law in a Hilbert space [Formula: see text], aiming to shed light on the acceleration phenomenon for monotone inclusion problems, which unifies a broad class of optimization, saddle point, and variational inequality (VI) problems under a single framework. Given an operator [Formula: see text] that is maximal monotone, we propose a closed-loop control system that is governed by the operator [Formula: see text], where a feedback law [Formula: see text] is tuned by the resolution of the algebraic equation [Formula: see text] for some [Formula: see text]. Our first contribution is to prove the existence and uniqueness of a global solution via the Cauchy–Lipschitz theorem. We present a simple Lyapunov function for establishing the weak convergence of trajectories via the Opial lemma and strong convergence results under additional conditions. We then prove a global ergodic convergence rate of [Formula: see text] in terms of a gap function and a global pointwise convergence rate of [Formula: see text] in terms of a residue function. Local linear convergence is established in terms of a distance function under an error bound condition. Further, we provide an algorithmic framework based on the implicit discretization of our system in a Euclidean setting, generalizing the large-step hybrid proximal extragradient framework. Even though the discrete-time analysis is a simplification and generalization of existing analyses for a bounded domain, it is largely motivated by the aforementioned continuous-time analysis, illustrating the fundamental role that the closed-loop control plays in acceleration in monotone inclusion. A highlight of our analysis is a new result concerning [Formula: see text]-order tensor algorithms for monotone inclusion problems, complementing the recent analysis for saddle point and VI problems. Funding: This work was supported in part by the Mathematical Data Science Program of the Office of Naval Research [Grant N00014-18-1-2764] and by the Vannevar Bush Faculty Fellowship Program [Grant N00014-21-1-2941]." @default.
• W4313591350 created "2023-01-06" @default.
• W4313591350 creator A5049812527 @default.
• W4313591350 creator A5083720030 @default.
• W4313591350 date "2023-01-04" @default.
• W4313591350 modified "2023-10-14" @default.
• W4313591350 title "Monotone Inclusions, Acceleration, and Closed-Loop Control" @default.
• W4313591350 cites W1487976166 @default.
• W4313591350 cites W1495915592 @default.
• W4313591350 cites W1512478894 @default.
• W4313591350 cites W1570963478 @default.
• W4313591350 cites W1768854696 @default.
• W4313591350 cites W1837565340 @default.
• W4313591350 cites W1966953121 @default.
• W4313591350 cites W1970033879 @default.
• W4313591350 cites W1970602566 @default.
• W4313591350 cites W1974485522 @default.
• W4313591350 cites W1988720110 @default.
• W4313591350 cites W199410564 @default.
• W4313591350 cites W2003327120 @default.
• W4313591350 cites W2012117745 @default.
• W4313591350 cites W2035436991 @default.
• W4313591350 cites W2037679050 @default.
• W4313591350 cites W2038497950 @default.
• W4313591350 cites W2039151776 @default.
• W4313591350 cites W2043093325 @default.
• W4313591350 cites W2052769657 @default.
• W4313591350 cites W2053487511 @default.
• W4313591350 cites W2056578325 @default.
• W4313591350 cites W2062016584 @default.
• W4313591350 cites W2062059813 @default.
• W4313591350 cites W2063357812 @default.
• W4313591350 cites W2075226379 @default.
• W4313591350 cites W2075803640 @default.
• W4313591350 cites W2084845949 @default.
• W4313591350 cites W2089559088 @default.
• W4313591350 cites W2094772768 @default.
• W4313591350 cites W2099679613 @default.
• W4313591350 cites W2104311270 @default.
• W4313591350 cites W2109628201 @default.
• W4313591350 cites W2123713848 @default.
• W4313591350 cites W2134656178 @default.
• W4313591350 cites W2145867192 @default.
• W4313591350 cites W2302721240 @default.
• W4313591350 cites W2317926736 @default.
• W4313591350 cites W2333372169 @default.
• W4313591350 cites W2501693933 @default.
• W4313591350 cites W2731666329 @default.
• W4313591350 cites W2735979640 @default.
• W4313591350 cites W2768527043 @default.
• W4313591350 cites W2771744050 @default.
• W4313591350 cites W2772443375 @default.
• W4313591350 cites W2788242395 @default.
• W4313591350 cites W2795507584 @default.
• W4313591350 cites W2808862920 @default.
• W4313591350 cites W2963353224 @default.
• W4313591350 cites W2963430672 @default.
• W4313591350 cites W2963505547 @default.
• W4313591350 cites W2964018031 @default.
• W4313591350 cites W2964216752 @default.
• W4313591350 cites W2965299328 @default.
• W4313591350 cites W2971643127 @default.
• W4313591350 cites W2977046017 @default.
• W4313591350 cites W3041815334 @default.
• W4313591350 cites W3047531400 @default.
• W4313591350 cites W3048765741 @default.
• W4313591350 cites W3085330744 @default.
• W4313591350 cites W3087406501 @default.
• W4313591350 cites W3102391325 @default.
• W4313591350 cites W3118261333 @default.
• W4313591350 cites W3120012157 @default.
• W4313591350 cites W3136523593 @default.
• W4313591350 cites W3136976430 @default.
• W4313591350 cites W3181590451 @default.
• W4313591350 cites W3182238355 @default.
• W4313591350 cites W3184876224 @default.
• W4313591350 cites W3185974649 @default.
• W4313591350 cites W3196133355 @default.
• W4313591350 cites W3208977561 @default.
• W4313591350 cites W4206097460 @default.
• W4313591350 cites W4238957126 @default.
• W4313591350 cites W4249667877 @default.
• W4313591350 cites W4253215513 @default.
• W4313591350 cites W46627373 @default.
• W4313591350 cites W84056083 @default.
• W4313591350 cites W84725740 @default.
• W4313591350 doi "https://doi.org/10.1287/moor.2022.1343" @default.
• W4313591350 hasPublicationYear "2023" @default.
• W4313591350 type Work @default.
• W4313591350 citedByCount "0" @default.
• W4313591350 crossrefType "journal-article" @default.
• W4313591350 hasAuthorship W4313591350A5049812527 @default.
• W4313591350 hasAuthorship W4313591350A5083720030 @default.
• W4313591350 hasBestOaLocation W43135913502 @default.
• W4313591350 hasConcept C121332964 @default.
• W4313591350 hasConcept C12715386 @default.
• W4313591350 hasConcept C134306372 @default.
• W4313591350 hasConcept C158622935 @default.
• W4313591350 hasConcept C22324862 @default.
• W4313591350 hasConcept C2524010 @default.

• next