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An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained by decomposing the objective function into convex and concave parts and replacing the concave part by an affine… (More)

This paper presents two fast algorithms for total variation–based image reconstruction in a magnetic resonance imaging technique known as partially parallel imaging (PPI), where the inversion matrix is large and ill-conditioned. These algorithms utilize variable splitting techniques to decou-ple the original problem into more easily solved subproblems. The… (More)

The convergence rate is analyzed for the sparse reconstruction by separable approximation (SpaRSA) algorithm for minimizing a sum f (x) + ψ(x), where f is smooth and ψ is convex, but possibly nonsmooth. It is shown that if f is convex, then the error in the objective function at iteration k is bounded by a/k for some a independent of k. Moreover, if the… (More)

—The optimal power flow is the problem of determining the most efficient, low-cost and reliable operation of a power system by dispatching the available electricity generation resources to the load on the system. Unlike the classical optimal power flow problem, the security-constrained optimal power flow (SCOPF) problem takes into account both the… (More)

We propose a two-stage stochastic version of the classical economic dispatch problem with alternating-current power flow constraints, a nonconvex optimization formulation that is central to power transmission and distribution over an electricity grid. Certain generation decisions made in the first stage cannot further be changed in the second stage, where… (More)

We propose a two-stage non-linear stochastic formulation for the economic dispatch problem under renewable-generation uncertainty. Each stage models dispatching and transmission decisions that are made on subsequent time periods. Certain generation decisions are made only in the first stage and the second stage realizes the actual renewable generation,… (More)

A branch and bound algorithm is developed for global optimization. Branching in the algorithm is accomplished by subdividing the feasible set using ellipses. Lower bounds are obtained by replacing the concave part of the objective function by an affine underestimate. A ball approximation algorithm, obtained by generalizing of a scheme of Lin and Han, is… (More)

We consider concave minimization problems over nonconvex sets. Optimization problems with this structure arise in sparse principal component analysis. We analyze both a gradient projection algorithm and an approximate Newton algorithm where the Hessian approximation is a multiple of the identity. Convergence results are established. In numerical experiments… (More)