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optimize -- solve a semidefinite program



This method solves a semidefinite programming problem. There is an interface to the solvers CSDP, SDPA and MOSEK. The default solver is CSDP, which is preinstalled with Macaulay2. Alternatively, there is rudimentary dual interior point method implemented entirely in Macaulay2 language.

i1 : P = sdp(matrix{{1,0},{0,2}}, matrix{{0,1},{1,0}}, matrix{{-1}});
i2 : (X,y,Z,stat) = optimize P;
i3 : y

o3 = | -1.41421 |

                1         1
o3 : Matrix RR    <-- RR
              53        53

References: Convex Optimization, Boyd, Vandenberghe, Cambridge University Press (2004), pp. 618-619, pp. 463-466.



The "M2" solver might fail if the dual problem is not strictly feasible. It also does not return the primal solution.

See also

Ways to use optimize :

For the programmer

The object optimize is a method function with options.