Convex Quantifier Elimination for Semidefinite Programming
نویسندگان
چکیده
Semidefinite Programming (SDP) is a class of convex optimization problems with a linear objective function and linear matrix inequality (LMI) constraints. SDP problems have many applications in engineering and applied mathematics. We propose a reasonably fast algorithm to prove and solve SDP exactly by exploiting the convexity of the SDP feasibility domain. This is achieved by combining a symbolic algorithm of cylindrical algebraic decomposition (CAD) and a lifting strategy that takes into account the convexity properties of SDP. The effectiveness of our method is examined by applying it to some examples on QEPCAD and maple.
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