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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)
This paper investigates a Lagrangian dual problem for solving the optimal power flow problem in rectangular form that arises from power system analysis. If strong duality does not hold for the dual, we propose two classes of branch-and-bound algorithms that guarantee to solve the problem to optimality. The lower bound for the objective function is obtained(More)
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 partially parallel magnetic resonance imaging (PPI) where the inversion matrix is large and ill-conditioned. These algorithms utilize variable splitting techniques to decouple the original problem into more easily solved subproblems. The first method reduces the image(More)
Motivated by the increasing complexity in the control of distribution level electric power systems especially in a smart grid environment, we propose fully decentralized algorithms to solve alternating current (AC) optimal power flow (OPF) problems. The key feature of the proposed algorithms is a complete decentralization of computation down to nodal level.(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)
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)
—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)
—The security-constrained optimal power flow problem considers both the normal state and contingency constraints, and it is formulated as a large-scale nonconvex optimization problem. We propose a global optimization algorithm based on Lagrangian duality to solve the nonconvex problem to optimality. As usual, the global approach is often time-consuming,(More)