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...l PSD splitting. For sizes above 1 We observed in our experiments that sometimes the SDP solver in CVX stops because of slow progress or a large gap. In such a case, we use the procedure described in =-=[17]-=- (coded by Kim-chuan Toh[30]) to find a rigorous lower bound for our relaxation model which further yields a lower bound for the underlying QAP. 14F-SVD S-SVD MSDR3 N//N+ Prob. Rgap CPU Rgap CPU Rgap...

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...r importance that each solver can be used, and the solver need not to produce any error bounds, neither in the forward nor in the backward error sense. This package implements techniques described in =-=[7]-=- and [8], and has several features: it computes verified lower and upper bounds of the optimal value for semidefinite programs, proves existence of feasible solutions, also for LMI’s, provides rigorou...

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...rtance that each solver can be used, and the solver need not produce any error bounds, neither in the forward nor in the backward error sense. This package implements techniques described in [11] and =-=[12]-=- and has several features: • computes verified lower and upper bounds of the optimal value for semidefinite programs, • proves existence of feasible and optimal solutions, also for LMI’s, • provides r...

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... rational numbers (Num library). It loads the A and B matrices and interacts with Scilab to compute the different sequence of calls to Scilab functions. 10There also exists guaranteed SDP solvers now =-=[14]-=- over and underapproximating the primal and the dual problem to guarantee an error bound on the result. However we only need to check the final result. Thanks to Éric Goubault for pointing that to us...

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...more efficient for the purpose of computing a lower bound for (22). We should mention that as the solver SDPNAL only produces an approximately primal-dual feasible solution for (22), the procedure in =-=[21]-=- is used to generate a valid lower bound v (0) LB for v (0) based on the approximately feasible solution. From the table, we may observe that the Lagrangian-DNN relaxation (12) of (23) can produce muc...

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...n of this algorithm can be found in the case of linear programming in [14], for smooth convex programming problems in [13], and for semidefinite programming problems and linear matrix inequalities in =-=[16]-=-. 5 Second Order Cone Programming In SOCP the partial ordering is defined by the ice-cream cone (9) yielding a finite dimensional vector lattice equipped with the following operations. Theorem 5.1 Let...

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... with the method of [18]. This avoided excessive memory requirements and also reduced the CPU time needed. A further enhancement applied, as in [14], is to compute verified bounds (see Jansson et al. =-=[10]-=-). In case the SDP solver does not quite finish with good accuracy the computed bound cannot be guaranteed be a lower bound although in most cases it will. To guarantee the bound interval-arithmetic m...