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—A fundamental problem in wireless ad–hoc and sensor networks is that of determining the positions of nodes. Often, such a problem is complicated by the presence of nodes whose positions cannot be uniquely determined. Most existing work uses the notion of global rigidity from rigidity theory to address the non–uniqueness issue. However, such a notion is not… (More)

Owing to their high accuracy and ease of formulation, there has been great interest in applying convex optimization techniques, particularly that of semidefinite programming (SDP) relaxation, to tackle the sensor network localization problem in recent years. However , a drawback of such techniques is that the resulting convex program is often expensive to… (More)

We consider a linear complementarity problem (LCP) arisen from the Arrow-Debreu-Leontief competitive economy equilibrium where the LCP coefficient matrix is symmetric. We prove that the decision problem, to decide whether or not there exists a complementary solution , is NP-complete. Under certain conditions, an LCP solution is guaranteed to exist and we… (More)

Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information–theoretic variant of the well–studied matrix completion problem, and the main objective is to design an efficient algorithm that… (More)

We report preliminary results on stochastic optimization with limited distributional information. Lack of complete distribution calls for stochastically robust models that, after exploiting available limited or partial information, offer risk-shielded solutions, i.e., solutions that are insensitive to all possible distributions of random variables. We focus… (More)

In this paper, we present an interior-point path-following algorithm for computing a Leontief economy equilibrium, that is, an exchange market equilibrium with Leontief utility functions, which is known to be in the complexity class of PPAD-complete. It is known that an equilibrium corresponds to a solution of a system of complementar-ities, so we construct… (More)

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