dc.contributor |
Universitat Politècnica de Catalunya. Departament de Ciències de la Computació |
dc.contributor.author |
Xhafa Xhafa, Fatos |
dc.contributor.author |
Navarro, Gonzalo |
dc.date |
1996-05-02 |
dc.identifier.citation |
Xhafa, F., Navarro, G. "A Maple package for semidefinite programming". 1996. |
dc.identifier.uri |
http://hdl.handle.net/2117/96476 |
dc.language.iso |
eng |
dc.relation |
R96-28 |
dc.rights |
info:eu-repo/semantics/openAccess |
dc.subject |
Àrees temàtiques de la UPC::Informàtica |
dc.subject |
Maple |
dc.subject |
Semidefinite programming |
dc.subject |
Optimization |
dc.subject |
Linear equality constraints |
dc.subject |
SP |
dc.title |
A Maple package for semidefinite programming |
dc.type |
info:eu-repo/semantics/publishedVersion |
dc.type |
info:eu-repo/semantics/report |
dc.description.abstract |
We present a package in Maple for solving
Semidefinite Programming. Semidefinite Programming (SP)
is the problem
of optimizing a linear function of a symmetric matrix
subject
to linear equality constraints and the condition that the
matrix of variables be positive semidefinite. SP
is strong enough to represent combinatorial problems
and very
recently, it has been used to obtain good approximation
algorithms
for several problems, namely Max Cut, Max 2SAT,
Graph Coloring, etc. All of them use the key fact that
SP can be solved in linear time (by either Ellipsoid
algorithms or Interior-Point algorithms).
We have implemented in Maple Language the Interior-Point
algorithm
of Alizadeh. The routines which solve the problem are
collected in a
Maple package, called semidefinite, which
can be used similarly and as easily as any
other Maple package (like linalg, for example).
It can be used by
users who have some knowledge of Maple (though few).
It can also be
executed from the system (outside Maple)
and therefore there is no
need of knowing Maple at all. The package
can be used either to test feasibility of a SP or to
find the optimal solution, when it is feasible. To the
best of our
knowledge this is the first program in Maple to solve SP. |