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Title: The deconvolution operation in convex analysis: An introduction

Abstract

Performing the infimal convolution of two functions is a frequent and useful operation in Convex Analysis: it is, to great extent, the dual operation of the addition; it serves (like other {open_quotes}convolutions{close_quotes} in Analysis) to regularize functions; it has nice geometrical and economic interpretations. The deconvolution of a (convex) function by another one is a new operation, firstly defined in clear-cut manner, which is to the infimal convolution what the subtraction is to the addition for real numbers; it appears in conjugating the difference of convex functions; it serves in solving explicitly convolution equations; it has an interpretation in terms of subtraction of epigraphs. Since its introduction, the deconvolution operation has been studied more thoroughly by the author and his former students or associates. What we intend to present here is a short (and, hopefully, pedagogical) introduction to the deconvolution operation, in a simplified setting. This can be viewed as a complement to chapter IV and X in the book.

Authors:
Publication Date:
OSTI Identifier:
457594
Resource Type:
Journal Article
Journal Name:
Cybernetics and Systems Analysis
Additional Journal Information:
Journal Volume: 30; Journal Issue: 4; Other Information: PBD: Mar 1995; TN: Translated from Kibernetika i Sistemnyi Analiz; No. 4, 97-104(Jul-Aug 1994)
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; FUNCTIONS; MATHEMATICAL OPERATORS; ALGORITHMS

Citation Formats

Hiriart-Urruty, J B. The deconvolution operation in convex analysis: An introduction. United States: N. p., 1995. Web.
Hiriart-Urruty, J B. The deconvolution operation in convex analysis: An introduction. United States.
Hiriart-Urruty, J B. 1995. "The deconvolution operation in convex analysis: An introduction". United States.
@article{osti_457594,
title = {The deconvolution operation in convex analysis: An introduction},
author = {Hiriart-Urruty, J B},
abstractNote = {Performing the infimal convolution of two functions is a frequent and useful operation in Convex Analysis: it is, to great extent, the dual operation of the addition; it serves (like other {open_quotes}convolutions{close_quotes} in Analysis) to regularize functions; it has nice geometrical and economic interpretations. The deconvolution of a (convex) function by another one is a new operation, firstly defined in clear-cut manner, which is to the infimal convolution what the subtraction is to the addition for real numbers; it appears in conjugating the difference of convex functions; it serves in solving explicitly convolution equations; it has an interpretation in terms of subtraction of epigraphs. Since its introduction, the deconvolution operation has been studied more thoroughly by the author and his former students or associates. What we intend to present here is a short (and, hopefully, pedagogical) introduction to the deconvolution operation, in a simplified setting. This can be viewed as a complement to chapter IV and X in the book.},
doi = {},
url = {https://www.osti.gov/biblio/457594}, journal = {Cybernetics and Systems Analysis},
number = 4,
volume = 30,
place = {United States},
year = {Wed Mar 01 00:00:00 EST 1995},
month = {Wed Mar 01 00:00:00 EST 1995}
}