Convergence of sequences: A survey

B. Franci; S. Grammatico

doi:10.1016/j.arcontrol.2022.01.003

Convergence of sequences: A survey

B. Franci^*, S. Grammatico

^*Corresponding author for this work

Research output: Contribution to journal › (Systematic) Review article › peer-review

Abstract

Convergent sequences of real numbers play a fundamental role in many different problems in system theory, e.g., in Lyapunov stability analysis, as well as in optimization theory and computational game theory. In this survey, we provide an overview of the literature on convergence theorems and their connection with Fejer monotonicity in the deterministic and stochastic settings, and we show how to exploit these results.

Original language	English
Pages (from-to)	161-186
Number of pages	26
Journal	Annual Reviews in Control
Volume	53
DOIs	https://doi.org/10.1016/j.arcontrol.2022.01.003
Publication status	Published - 2022

Keywords

Convergence
STOCHASTIC-APPROXIMATION METHODS
BACKWARD SPLITTING METHOD
FIXED-POINT ITERATIONS
MONOTONE INCLUSIONS
CONVEX-OPTIMIZATION
VARIANCE REDUCTION
DYNAMICAL-SYSTEMS
GRADIENT METHODS
ALGORITHMS
REGULARIZATION

Access to Document

10.1016/j.arcontrol.2022.01.003Licence: CC BY

Cite this

@article{acefe166bc0b44179fc15568aa3e34b6,

title = "Convergence of sequences: A survey",

abstract = "Convergent sequences of real numbers play a fundamental role in many different problems in system theory, e.g., in Lyapunov stability analysis, as well as in optimization theory and computational game theory. In this survey, we provide an overview of the literature on convergence theorems and their connection with Fejer monotonicity in the deterministic and stochastic settings, and we show how to exploit these results.",

keywords = "Convergence, STOCHASTIC-APPROXIMATION METHODS, BACKWARD SPLITTING METHOD, FIXED-POINT ITERATIONS, MONOTONE INCLUSIONS, CONVEX-OPTIMIZATION, VARIANCE REDUCTION, DYNAMICAL-SYSTEMS, GRADIENT METHODS, ALGORITHMS, REGULARIZATION",

author = "B. Franci and S. Grammatico",

year = "2022",

doi = "10.1016/j.arcontrol.2022.01.003",

language = "English",

volume = "53",

pages = "161--186",

journal = "Annual Reviews in Control",

issn = "1367-5788",

publisher = "Elsevier Limited",

}

TY - JOUR

T1 - Convergence of sequences: A survey

AU - Franci, B.

AU - Grammatico, S.

PY - 2022

Y1 - 2022

N2 - Convergent sequences of real numbers play a fundamental role in many different problems in system theory, e.g., in Lyapunov stability analysis, as well as in optimization theory and computational game theory. In this survey, we provide an overview of the literature on convergence theorems and their connection with Fejer monotonicity in the deterministic and stochastic settings, and we show how to exploit these results.

AB - Convergent sequences of real numbers play a fundamental role in many different problems in system theory, e.g., in Lyapunov stability analysis, as well as in optimization theory and computational game theory. In this survey, we provide an overview of the literature on convergence theorems and their connection with Fejer monotonicity in the deterministic and stochastic settings, and we show how to exploit these results.

KW - Convergence

KW - STOCHASTIC-APPROXIMATION METHODS

KW - BACKWARD SPLITTING METHOD

KW - FIXED-POINT ITERATIONS

KW - MONOTONE INCLUSIONS

KW - CONVEX-OPTIMIZATION

KW - VARIANCE REDUCTION

KW - DYNAMICAL-SYSTEMS

KW - GRADIENT METHODS

KW - ALGORITHMS

KW - REGULARIZATION

U2 - 10.1016/j.arcontrol.2022.01.003

DO - 10.1016/j.arcontrol.2022.01.003

M3 - (Systematic) Review article

SN - 1367-5788

VL - 53

SP - 161

EP - 186

JO - Annual Reviews in Control

JF - Annual Reviews in Control

ER -