# Tag Info

## Hot answers tagged sdp

5

EDIT: Per comment below by YALMIP deveeloper Johan Lofberg, the bug in YALMIP was a typo, which has now been corrected and available at https://github.com/yalmip/YALMIP/archive/develop.zip . Using this newest develop version of YALMIP, Mosek should now be able to solve the problem. Edited to reflect YALMIP developer's acknowledgement that there is a bug in ...

3

The following is from Section 2.2 of Semidefinite Programming for Combinatorial Optimization by Christoph Helmberg. Let's define \begin{align*} p^* &= \inf\{\langle C,X\rangle\,:\,X\text{ primal feasible}\},\\ d^* &= \sup\{\langle b,y\rangle\,:\,y\text{ dual feasible}\}. \end{align*} In particular, $p^*=\infty$ if the primal is infeasible, \$d^*=-\...

1

I now believe the answer is yes. I.e., at least one optimal solution will lie at an extreme point. See Hermann Schichl's answer here. For a minimization problem, you need a convex objective function on a convex domain. For a maximization problem, the objective function must instead be concave. Since SDPs have a linear objective function and a convex feasible ...

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