{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T17:56:41Z","timestamp":1754157401571,"version":"3.41.2"},"reference-count":8,"publisher":"Emerald","issue":"5","license":[{"start":{"date-parts":[[2009,6,12]],"date-time":"2009-06-12T00:00:00Z","timestamp":1244764800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,6,12]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-heading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to solve a global optimization problem raised from industry, named the <jats:italic>M<\/jats:italic>\u2010problem, posed in the space <jats:italic>L<\/jats:italic><jats:sub>1<\/jats:sub> of Lebesgue measurable functions of integrable absolute value.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>The paper introduces the new concept of <jats:italic>V\u2010<\/jats:italic>dense curve (VDC), a generalization of that of <jats:italic>\u03b1<\/jats:italic>\u2010dense curve, to densify subsets of topological vector spaces not necessarily metrisable. It is proved that the feasible set of the <jats:italic>M<\/jats:italic>\u2010problem, namely the subset <jats:italic>D<\/jats:italic> of <jats:italic>L<\/jats:italic><jats:sub>1<\/jats:sub> of all probability functions, is densifiable by VDC provided that <jats:italic>L<\/jats:italic><jats:sub>1<\/jats:sub> to be endowed with the weak topology.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>It is proved that the <jats:italic>M<\/jats:italic>\u2010problem, consisting of finding a probability function <jats:italic>f<\/jats:italic> of <jats:italic>D<\/jats:italic> associated to the mean life of an electronic devise that minimizes the expectation defined by a certain functional on <jats:italic>L<\/jats:italic><jats:sub>1<\/jats:sub>, is not a well\u2010posed problem in <jats:italic>D<\/jats:italic>. Nevertheless, by virtue of the compactness, the <jats:italic>M<\/jats:italic>\u2010problem has solution on each weak VDC in <jats:italic>D<\/jats:italic> for arbitrary weak 0\u2010neighbourhood <jats:italic>V<\/jats:italic>, which allows to find an approximate probability function with arbitrary precision.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>The paper has designed, by means of the VDC\u2010method, a convergent algorithm to find approximate solutions in ill\u2010posed global optimization problems when the feasible set is contained in a non\u2010metrisable topological vector space.<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684920910962605","type":"journal-article","created":{"date-parts":[[2009,7,4]],"date-time":"2009-07-04T07:03:34Z","timestamp":1246691014000},"page":"709-717","source":"Crossref","is-referenced-by-count":0,"title":["Global optimization by <i>V<\/i>\u2010dense curves in topological vector spaces"],"prefix":"10.1108","volume":"38","author":[{"given":"Gaspar","family":"Mora","sequence":"first","affiliation":[]}],"member":"140","reference":[{"key":"key2022031420280235900_b1","doi-asserted-by":"crossref","unstructured":"Carothers, N.L. (2005), A Short Course on Banach Space Theory, Cambridge University Press, Cambridge.","DOI":"10.1017\/CBO9780511614057"},{"key":"key2022031420280235900_b2","unstructured":"Cherruault, Y. and Mora, G. (2005), Optimisation Globale. Theorie des Courbes Alpha\u2010Denses, Economica, Paris."},{"key":"key2022031420280235900_b3","unstructured":"Hocking, J.G. and Young, G.S. (1961), Topology, Addison\u2010Wesley, Reading, MA."},{"key":"key2022031420280235900_b4","unstructured":"Kelly, J.L. (1955), General Topology, 2nd ed., Springer, New York, NY."},{"key":"key2022031420280235900_b5","doi-asserted-by":"crossref","unstructured":"Megginson, R.E. (1998), An Introduction to Banach Spaces, Springer, New York, NY.","DOI":"10.1007\/978-1-4612-0603-3"},{"key":"key2022031420280235900_b6","unstructured":"Mora, G. and Mira, J.A. (2003), \u201cAlpha\u2010dense curves in infinite dimensional spaces\u201d, International Journal of Pure and Applied Mathematics, Vol. 5 No. 4, pp. 437\u201049."},{"key":"key2022031420280235900_b7","doi-asserted-by":"crossref","unstructured":"Schaefer, H.H. (1971), Topological Vector Spaces, Springer, New York, NY.","DOI":"10.1007\/978-1-4684-9928-5"},{"key":"key2022031420280235900_b8","doi-asserted-by":"crossref","unstructured":"Tricot, C. (1995), Curves and Fractal Dimension, Springer, New York, NY.","DOI":"10.1007\/978-1-4612-4170-6"}],"container-title":["Kybernetes"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.emeraldinsight.com\/doi\/full-xml\/10.1108\/03684920910962605","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/03684920910962605\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/03684920910962605\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T23:53:37Z","timestamp":1753401217000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/k\/article\/38\/5\/709-717\/273437"}},"subtitle":[],"editor":[{"given":"Yves","family":"Cherruault","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2009,6,12]]},"references-count":8,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2009,6,12]]}},"alternative-id":["10.1108\/03684920910962605"],"URL":"https:\/\/doi.org\/10.1108\/03684920910962605","relation":{},"ISSN":["0368-492X"],"issn-type":[{"type":"print","value":"0368-492X"}],"subject":[],"published":{"date-parts":[[2009,6,12]]}}}