eprintid: 4252
rev_number: 7
eprint_status: archive
userid: 351
dir: disk0/00/00/42/52
datestamp: 2016-01-15 02:05:04
lastmod: 2021-08-27 17:35:55
status_changed: 2016-01-15 02:05:04
type: article
metadata_visibility: show
item_issues_count: 1
creators_name: Ermoliev, Y.M.
creators_name: Norkin, V.I.
creators_name: Wets, R.J.-B.
creators_id: 1445
creators_id: AL1055
creators_id: AL1370
title: The minimization of semicontinuous functions: Mollifier subgradients
ispublished: pub
internal_subjects: iis_mod
internal_subjects: iis_met
divisions: prog_rpc
keywords: impulse control; discrete events systems; averaged functions; subgradients; subdifferentiability; stochastic quasi-gradients; epi-convergence
abstract: To minimize discontinuous functions that arise in the context of systems with jumps, for example, we propose a new approach based on approximation via averaged functions (obtained by convolution with mollifiers). The properties of averaged functions are studied, after it is shown that they can be used in an approximation scheme consistent with minimization. A new notion of subgradient is introduced based on approximations generated by mollifiers and is exploited in the design of minimization procedures.
date: 1995
date_type: published
publisher: Society for Industrial and Applied Mathematics (SIAM)
id_number: 10.1137/S0363012992238369
iiasapubid: XJ-95-082
iiasa_bibref: SIAM Journal of Control Optimization; 33(1):149-167 [1995]
iiasa_bibnotes: [doi:10.1137/S0363012992238369]
creators_browse_id: 338
creators_browse_id: 2245
creators_browse_id: 2512
full_text_status: none
publication: SIAM Journal on Control and Optimization
volume: 33
number: 1
pagerange: 149-167
refereed: TRUE
issn: 1095-7138
related_url_url: http://siamdl.aip.org/dbt/dbt.jsp?KEY=SJCODC
related_url_type: pub
coversheets_dirty: FALSE
fp7_type: info:eu-repo/semantics/article
citation:   Ermoliev, Y.M. <https://pure.iiasa.ac.at/view/iiasa/338.html>, Norkin, V.I. <https://pure.iiasa.ac.at/view/iiasa/2245.html>, & Wets, R.J.-B. <https://pure.iiasa.ac.at/view/iiasa/2512.html>  (1995).  The minimization of semicontinuous functions: Mollifier subgradients.   SIAM Journal on Control and Optimization 33 (1) 149-167. 10.1137/S0363012992238369 <https://doi.org/10.1137/S0363012992238369>.