On the Structure of Convex Piecewise Quadratic Functions
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...
| Main Author: | |
|---|---|
| Format: | Journal Article |
| Language: | English |
| Published: |
Springer New York LLC
1992
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/91446 |
| _version_ | 1848765522900942848 |
|---|---|
| author | Sun, Jie |
| author_facet | Sun, Jie |
| author_sort | Sun, Jie |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T11:36:36Z |
| format | Journal Article |
| id | curtin-20.500.11937-91446 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:36:36Z |
| publishDate | 1992 |
| publisher | Springer New York LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-914462023-04-20T05:42:32Z On the Structure of Convex Piecewise Quadratic Functions Sun, Jie Science & Technology Technology Physical Sciences Operations Research & Management Science Mathematics, Applied Mathematics CONVEX POLYHEDRA EXTENDED LINEAR-QUADRATIC PROGRAMS MONOTROPIC PROGRAMMING PIECEWISE QUADRATIC FUNCTIONS SEPARABILITY OF FUNCTIONS 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. 1992 Journal Article http://hdl.handle.net/20.500.11937/91446 10.1007/BF00939839 English Springer New York LLC fulltext |
| spellingShingle | Science & Technology Technology Physical Sciences Operations Research & Management Science Mathematics, Applied Mathematics CONVEX POLYHEDRA EXTENDED LINEAR-QUADRATIC PROGRAMS MONOTROPIC PROGRAMMING PIECEWISE QUADRATIC FUNCTIONS SEPARABILITY OF FUNCTIONS Sun, Jie On the Structure of Convex Piecewise Quadratic Functions |
| title | On the Structure of Convex Piecewise Quadratic Functions |
| title_full | On the Structure of Convex Piecewise Quadratic Functions |
| title_fullStr | On the Structure of Convex Piecewise Quadratic Functions |
| title_full_unstemmed | On the Structure of Convex Piecewise Quadratic Functions |
| title_short | On the Structure of Convex Piecewise Quadratic Functions |
| title_sort | on the structure of convex piecewise quadratic functions |
| topic | Science & Technology Technology Physical Sciences Operations Research & Management Science Mathematics, Applied Mathematics CONVEX POLYHEDRA EXTENDED LINEAR-QUADRATIC PROGRAMS MONOTROPIC PROGRAMMING PIECEWISE QUADRATIC FUNCTIONS SEPARABILITY OF FUNCTIONS |
| url | http://hdl.handle.net/20.500.11937/91446 |