Global Optimization with Polynomials
The class of POP (Polynomial Optimization Problems) covers a wide rang of optimization problems such as 0 - 1 integer linear and quadratic programs, nonconvex quadratic programs and bilinear matrix inequalities. In this paper, we review some methods on solving the unconstraint case: minimize a real-...
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| Format: | Article |
| Language: | en_US |
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2003
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| Online Access: | http://hdl.handle.net/1721.1/3883 |
| _version_ | 1811093730293186560 |
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| author | Han, Deren |
| author_facet | Han, Deren |
| author_sort | Han, Deren |
| collection | MIT |
| description | The class of POP (Polynomial Optimization Problems) covers a wide rang of optimization problems such as 0 - 1 integer linear and quadratic programs, nonconvex quadratic programs and bilinear matrix inequalities. In this paper, we review some methods on solving the unconstraint case: minimize a real-valued polynomial p(x) : Rn â R, as well the constraint case: minimize p(x) on a semialgebraic set K, i.e., a set defined by polynomial equalities and inequalities. We also summarize some questions that we are currently considering. |
| first_indexed | 2024-09-23T15:49:43Z |
| format | Article |
| id | mit-1721.1/3883 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:49:43Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | mit-1721.1/38832019-04-12T08:36:44Z Global Optimization with Polynomials Han, Deren Polynomial Optimization Problems Semidefinite Programming Second-Order-Cone-Programming LP relaxation The class of POP (Polynomial Optimization Problems) covers a wide rang of optimization problems such as 0 - 1 integer linear and quadratic programs, nonconvex quadratic programs and bilinear matrix inequalities. In this paper, we review some methods on solving the unconstraint case: minimize a real-valued polynomial p(x) : Rn â R, as well the constraint case: minimize p(x) on a semialgebraic set K, i.e., a set defined by polynomial equalities and inequalities. We also summarize some questions that we are currently considering. Singapore-MIT Alliance (SMA) 2003-12-14T22:39:43Z 2003-12-14T22:39:43Z 2004-01 Article http://hdl.handle.net/1721.1/3883 en_US High Performance Computation for Engineered Systems (HPCES); 121672 bytes application/pdf application/pdf |
| spellingShingle | Polynomial Optimization Problems Semidefinite Programming Second-Order-Cone-Programming LP relaxation Han, Deren Global Optimization with Polynomials |
| title | Global Optimization with Polynomials |
| title_full | Global Optimization with Polynomials |
| title_fullStr | Global Optimization with Polynomials |
| title_full_unstemmed | Global Optimization with Polynomials |
| title_short | Global Optimization with Polynomials |
| title_sort | global optimization with polynomials |
| topic | Polynomial Optimization Problems Semidefinite Programming Second-Order-Cone-Programming LP relaxation |
| url | http://hdl.handle.net/1721.1/3883 |
| work_keys_str_mv | AT handeren globaloptimizationwithpolynomials |