Marcia Fampa

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We consider a new nonlinear relaxation for the Constrained Maximum-Entropy Sampling Problem { the problem of choosing the s s principal submatrix with maximal determinant from a given n n positive deenite matrix, subject to linear constraints. We implement a branch-and-bound algorithm for the problem, using the new relaxation. The performance on test(More)
We describe improvements to Smith's branch-and-bound (B&B) algorithm for the Euclidean Steiner problem in IR d. Nodes in the B&B tree correspond to full Steiner topologies associated with a subset of the terminal nodes, and branching is accomplished by " merging " a new terminal node with each edge in the current Steiner tree. For a given topology we use a(More)
We consider a new nonlinear relaxation for the Constrained Maximum Entropy Sampling Problem { the problem of choosing the s s principal submatrix with maximal determinant from a given n n positive deenite matrix, subject to linear constraints. We implement a branch-and-bound algorithm for the problem, using the new relaxation. The performance on test(More)
We consider the \remote{sampling" problem of choosing a subset S, with jSj = s, from a set N of observable random variables so as to obtain as much information as possible about a set T of target random variables which are not directly observable. Our criterion is that of minimizing the entropy of T conditioned on S. We connne our attention to the case in(More)
We present a new mathematical programming formulation for the Steiner minimal tree problem. We relax the integrality constraints on this formulation and transform the resulting problem (which is convex, but not everywhere differentiable) into a standard convex programming problem in conic form. We consider an efficient computation of an ε-optimal solution(More)
The Euclidean Steiner Tree Problem in dimension greater than 2 is notoriously difficult. Successful methods for exact solution are not based on mathematical-optimization — rather, they involve very sophisticated enumeration. There are two types of mathematical-optimization formulations in the literature, and it is an understatement to say that neither(More)