On the Structure of Convex Piecewise Quadratic Functions
dc.contributor.author | Sun, Jie | |
dc.date.accessioned | 2023-04-16T11:29:42Z | |
dc.date.available | 2023-04-16T11:29:42Z | |
dc.date.issued | 1992 | |
dc.identifier.citation | Sun, J. 1992. On the Structure of Convex Piecewise Quadratic Functions. Journal of Optimization Theory and Applications. 72 (3): pp. 499-510. | |
dc.identifier.uri | http://hdl.handle.net/20.500.11937/91446 | |
dc.identifier.doi | 10.1007/BF00939839 | |
dc.description.abstract |
Convex piecewise quadratic functions (CPQF) play an important role in mathematical programming, and yet their structure has not been fully studied. In this paper, these functions are categorized into difference-definite and difference-indefinite types. We show that, for either type, the expressions of a CPQF on neighboring polyhedra in its domain can differ only by a quadratic function related to the common boundary of the polyhedra. Specifically, we prove that the monitoring function in extended linear-quadratic programming is difference-definite. We then study the case where the domain of the difference-definite CPQF is a union of boxes, which arises in many applications. We prove that any such function must be a sum of a convex quadratic function and a separable CPQF. Hence, their minimization problems can be reformulated as monotropic piecewise quadratic programs. © 1992 Plenum Publishing Corporation. | |
dc.language | English | |
dc.publisher | Springer New York LLC | |
dc.subject | Science & Technology | |
dc.subject | Technology | |
dc.subject | Physical Sciences | |
dc.subject | Operations Research & Management Science | |
dc.subject | Mathematics, Applied | |
dc.subject | Mathematics | |
dc.subject | CONVEX POLYHEDRA | |
dc.subject | EXTENDED LINEAR-QUADRATIC PROGRAMS | |
dc.subject | MONOTROPIC PROGRAMMING | |
dc.subject | PIECEWISE QUADRATIC FUNCTIONS | |
dc.subject | SEPARABILITY OF FUNCTIONS | |
dc.title | On the Structure of Convex Piecewise Quadratic Functions | |
dc.type | Journal Article | |
dcterms.source.volume | 72 | |
dcterms.source.number | 3 | |
dcterms.source.startPage | 499 | |
dcterms.source.endPage | 510 | |
dcterms.source.issn | 0022-3239 | |
dcterms.source.title | Journal of Optimization Theory and Applications | |
dcterms.source.place | United States | |
dc.date.updated | 2023-04-16T11:29:42Z | |
curtin.department | School of Elec Eng, Comp and Math Sci (EECMS) | |
curtin.accessStatus | Open access | |
curtin.faculty | Faculty of Science and Engineering | |
curtin.contributor.orcid | Sun, Jie [0000-0001-5611-1672] | |
curtin.contributor.researcherid | Sun, Jie [B-7926-2016] [G-3522-2010] | |
dcterms.source.eissn | 1573-2878 | |
curtin.contributor.scopusauthorid | Sun, Jie [16312754600] [57190212842] | |
curtin.repositoryagreement | V3 |