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A symmetric matrix A is completely positive (CP) if there exists an entrywise nonnegative matrix B such that A = BB . We characterize the interior of the CP cone. We formulate the problem as linear optimizations with cones of moments. A semidefinite algorithm is proposed for checking interiors of the CP cone, and its properties are studied. A(More)
In this paper, a new nonlinear conjugate gradient method is proposed for large-scale unconstrained optimization. The sufficient descent property holds without any line searches. We use some steplength technique which ensures the Zoutendijk condition to be held, this method is proved to be globally convergent. Finally, we improve it, and do further analysis.
The combination technique is a method to reduce the computational time in the numerical approximation of partial diierential equations. In this paper, we prove the convergence of the combination technique for general second order elliptic diierential equations in two dimensions. Furthermore , the technique presented here can be applied to prove the(More)
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