{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T16:35:16Z","timestamp":1649176516467},"reference-count":11,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2020,2,24]],"date-time":"2020-02-24T00:00:00Z","timestamp":1582502400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,2,24]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The problem of maximizing a linear function with linear and quadratic constraints is considered. The solution of the problem is obtained in a constructive form using the Lagrange function and the optimality conditions. Many optimization problems can be reduced to the problem of this type. In this paper, as an application, we consider an improper linear programming problem formalized in the form of maximization of the initial linear criterion with a restriction to the Euclidean norm of the correction vector of the right-hand side of the constraints or the Frobenius norm of the correction matrix of both sides of the constraints.<\/jats:p>","DOI":"10.1515\/comp-2020-0005","type":"journal-article","created":{"date-parts":[[2020,2,25]],"date-time":"2020-02-25T09:01:15Z","timestamp":1582621275000},"page":"48-55","source":"Crossref","is-referenced-by-count":0,"title":["Linear-quadratic programming and its application to data correction of improper linear programming problems"],"prefix":"10.1515","volume":"10","author":[{"given":"Victor","family":"Gorelik","sequence":"first","affiliation":[{"name":"Dorodnicyn Computing Centre FRC CSC RAS,Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tatiana","family":"Zolotova","sequence":"additional","affiliation":[{"name":"Financial University under the Government of RF,Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","reference":[{"key":"ref01","first-page":"1","article-title":"Interior point methods in semidenite programming with applications to combinatorial optimization on Optimization","author":"Alizadeh","year":"1995","journal-title":"SIAM Journal"},{"key":"ref31","article-title":"ev Improper linear and convex programming problems","author":"Eremin","year":"1983"},{"key":"ref101","article-title":"Editors Encyclopedia of Optimization","volume":"11","author":"Floudas","year":"2009"},{"key":"ref81","first-page":"1","article-title":"programming with one negative eigenvalue is hard of Optimization","author":"Pardalos","year":"1991","journal-title":"Journal Global"},{"key":"ref41","first-page":"11","article-title":"correction of a linear programming problem with inconsistent constraints and","author":"Gorelik","year":"2001","journal-title":"Matrix Computational Mathematics Mathematical Physics"},{"key":"ref61","first-page":"2017","article-title":"The problem of linear - quadratic programming In of th International Conference on Optimization and Applications","volume":"7","author":"Gorelik","year":"2017","journal-title":"Proceedings October"},{"key":"ref111","first-page":"75","article-title":"On solving a linear program with one quadratic constraint Decisions in","volume":"12","author":"Martein","year":"1987","journal-title":"Economics Finance"},{"key":"ref51","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1134\/S0965542507040033","article-title":"correction of a dual pair of improper linear programming problems and","volume":"47","author":"Erohin","year":"2007","journal-title":"Matrix Computational Mathematics Mathematical Physics"},{"key":"ref71","first-page":"1","article-title":"Approximation of the improper linear programming problem with restriction on the norm of the correction matrix of the left - hand side of the constraints In of th International Conference on Optimization and Applications DEStech Transactions on Computer","volume":"8","author":"Gorelik","year":"2018","journal-title":"Proceedings October Science Engineering"},{"key":"ref11","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1137\/0717073","article-title":"Loan An analysis of the total least squares problems","volume":"17","author":"Golub","year":"1980","journal-title":"SIAM Numer Anal"},{"key":"ref21","first-page":"149","article-title":"Algebraic relationships between classical regression and total least - squares estimation Linear Algebra and its Applications","author":"Van Huffel","year":"1987"}],"container-title":["Open Computer Science"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/comp\/10\/1\/article-p48.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/downloadpdf\/journals\/comp\/10\/1\/article-p48.xml","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T03:22:34Z","timestamp":1614482554000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/comp-2020-0005\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,24]]},"references-count":11,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.1515\/comp-2020-0005","relation":{},"ISSN":["2299-1093"],"issn-type":[{"value":"2299-1093","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,24]]}}}