Linear programming with positive semi-definite matrices
<p>We consider the general linear programming problem over the cone of positive semi-definite matrices. We first provide a simple sufficient condition for existence of optimal solutions and absence of a duality gap without requiring existence of a strictly feasible solution. We then simply cha...
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Hindawi Limited
1996-01-01
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| Series: | Mathematical Problems in Engineering |
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| Online Access: | http://www.hindawi.net/access/get.aspx?journal=mpe&volume=2&pii=S1024123X96000452 |
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doaj-4b27ff32b0714cacb65cdf8f2751309c2020-11-24T23:29:53ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51471996-01-0126499522Linear programming with positive semi-definite matricesLasserre J. B.<p>We consider the general linear programming problem over the cone of positive semi-definite matrices. We first provide a simple sufficient condition for existence of optimal solutions and absence of a duality gap without requiring existence of a strictly feasible solution. We then simply characterize the analogues of the standard concepts of linear programming, i.e., extreme points, basis, reduced cost, degeneracy, pivoting step as well as a Simplex-like algorithm.</p> http://www.hindawi.net/access/get.aspx?journal=mpe&volume=2&pii=S1024123X96000452Positive semi-definite matriceslinear programmingsimplex algorithm |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Lasserre J. B. |
| spellingShingle |
Lasserre J. B. Linear programming with positive semi-definite matrices Mathematical Problems in Engineering Positive semi-definite matrices linear programming simplex algorithm |
| author_facet |
Lasserre J. B. |
| author_sort |
Lasserre J. B. |
| title |
Linear programming with positive semi-definite matrices |
| title_short |
Linear programming with positive semi-definite matrices |
| title_full |
Linear programming with positive semi-definite matrices |
| title_fullStr |
Linear programming with positive semi-definite matrices |
| title_full_unstemmed |
Linear programming with positive semi-definite matrices |
| title_sort |
linear programming with positive semi-definite matrices |
| publisher |
Hindawi Limited |
| series |
Mathematical Problems in Engineering |
| issn |
1024-123X 1563-5147 |
| publishDate |
1996-01-01 |
| description |
<p>We consider the general linear programming problem over the cone of positive semi-definite matrices. We first provide a simple sufficient condition for existence of optimal solutions and absence of a duality gap without requiring existence of a strictly feasible solution. We then simply characterize the analogues of the standard concepts of linear programming, i.e., extreme points, basis, reduced cost, degeneracy, pivoting step as well as a Simplex-like algorithm.</p> |
| topic |
Positive semi-definite matrices linear programming simplex algorithm |
| url |
http://www.hindawi.net/access/get.aspx?journal=mpe&volume=2&pii=S1024123X96000452 |
| work_keys_str_mv |
AT lasserrejb linearprogrammingwithpositivesemidefinitematrices |
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