USLOVI OPTIMALNOSTI ZA IZOPERIMETRIJSKE PROBLEME OPTIMIZACIJE SA NEPREKIDNIM VREMENOM

eLibrary

 
 

USLOVI OPTIMALNOSTI ZA IZOPERIMETRIJSKE PROBLEME OPTIMIZACIJE SA NEPREKIDNIM VREMENOM

Show simple item record

dc.contributor.advisor Marinković, Boban
dc.contributor.author Vicanović, Jelena
dc.date.accessioned 2024-05-07T13:44:04Z
dc.date.available 2024-05-07T13:44:04Z
dc.date.issued 2024-04-24
dc.identifier.uri http://hdl.handle.net/123456789/5676
dc.description.abstract A convex continuous-time maximization problem is formulated and the nec- essary optimality conditions in the infinite-dimensional case are obtained. As a main tool for obtaining optimal conditions in this dissertation we use the new theorem of the alternative. Since there’s no a differentiability assumption, we perform a linearization of the problem using subdifferentials. It is proved that the multiplier with the objective function won’t be equal to zero. It was also shown that if the linear and non-linear constraints are separated, with additional assumptions it can be guaranteed that the multiplier with non-linear constraints will also be non-zero. In the following, an integral constraint is added to the original convex problem, so that a Lyapunov-type problem, i.e. an isoperimetric problem, is considered. Lin- earization of the problem using subdifferentials proved to be a practical way to ignore the lack of differentiability, so the optimality conditions were derived in a similar way. It is shown that the obtained results will also be valid for the vector case of the isoperimetric problem. Additionally, the optimality conditions for the smooth problem were considered. On the minimization problem, it was shown that the necessary conditions of Karush-Kuhn-Tucker type will be valid with the additional regularity constraint condition. Also, any point that satisfies the mentioned optimality conditions will be a global minimum. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2024-05-07T13:44:04Z No. of bitstreams: 1 J.Vicanovic_doktorska_disertacija.pdf: 2198434 bytes, checksum: 16c345f0e88b29ebc23bcd1cfbce3fa3 (MD5) en
dc.description.provenance Made available in DSpace on 2024-05-07T13:44:04Z (GMT). No. of bitstreams: 1 J.Vicanovic_doktorska_disertacija.pdf: 2198434 bytes, checksum: 16c345f0e88b29ebc23bcd1cfbce3fa3 (MD5) Previous issue date: 2024-04-24 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title USLOVI OPTIMALNOSTI ZA IZOPERIMETRIJSKE PROBLEME OPTIMIZACIJE SA NEPREKIDNIM VREMENOM en_US
mf.author.birth-date 1987-03-29
mf.author.birth-place Beograd en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srpkinja en_US
mf.subject.area Mathematics en_US
mf.subject.keywords Continuous-time programming, Convex programming, Optimality condi- tions, Theorems of the alternative, Isoperimetric problems, Multiobjective continuous-time programming problems en_US
mf.subject.subarea Optimization en_US
mf.contributor.committee Savić, Aleksandar
mf.contributor.committee Jović, Aleksandar
mf.contributor.committee Gajić, Borislav
mf.university.faculty Mathematical Faculty en_US
mf.document.references 82 en_US
mf.document.pages 62 en_US
mf.document.location Belgrade en_US
mf.document.genealogy-project No en_US
mf.university Belgrade University en_US

Files in this item

Files Size Format View
J.Vicanovic_doktorska_disertacija.pdf 2.198Mb PDF View/Open

This item appears in the following Collection(s)

Show simple item record