Large-scale smart grids call for online algorithms that are able to achieve the most accurate estimates. This paper shows how to achieve both the scalability and near globally optimal results for bad data and topology error detection and identification problems, by conducting fully distributed algorithms over convexified problem formulations. The proposed distributed decomposition is realized b...

For a wide class of problems in continuum mechanics like those involving phase transitions or finite elastoplasticity, the governing potentials tend to be not quasiconvex. This leads to the occurrence of microstructures of in principle arbitrarily small scale, which cannot be resolved by standard discretization schemes. Their effective macroscopic properties, however, can efficiently be recover...

We propose a sequential method to estimate monotone convex function that consists of: (i) monotone regression via solving a constrained least square problem and (ii) convexification of the monotone regression estimate via solving an associated constrained uniform approximation problem. We show that this method is faster than the constrained least squares (LS) method. The ratio of computation ti...

This paper focuses on solving two-stage stochastic mixed integer programs (SMIPs) with general mixed integer decision variables in both stages. We develop a decomposition algorithm in which the first stage approximation is solved using a branch-and-bound tree with nodes inheriting Benders’ cuts that are valid for their ancestor nodes. In addition, we develop two closely related convexification ...

We study the simultaneous convexification of graphs of bilinear functions gk(x;y) = yTAkx over x ∈ Ξ = {x ∈ [0, 1]n |Ex ≥ f} and y ∈ ∆m = { y ∈ R+ ∣∣1Ty ≤ 1}. We propose a constructive procedure to obtain a linear description of the convex hull of the resulting set. This procedure can be applied to derive convex and concave envelopes of certain bilinear functions, to study unary expansions of i...

We derive two theorems combining existence with necessary conditions for the relaxed unilateral problem of the optimal control of ordinary differential equations in which the functions that define the problem are Lipschitz-continuous in the state variables. These theorems generalize the results presented in a previous paper [8] by the addition of unilateral constraints on the state and control ...

We provide sufficient conditions for revenue maximization in a two-good monopoly where the buyer’s values for the items come from independent (but not necessarily identical) distributions over bounded intervals. Under certain distributional assumptions, we give exact, closed-form formulas for the prices and allocation rule of the optimal selling mechanism. As a side result we give the first exa...

We study the trust region subproblem (TRS) of minimizing a nonconvex quadratic function over the unit ball with additional conic constraints. Despite having a nonconvex objective, it is known that the TRS and a number of its variants are polynomial-time solvable. In this paper, we follow a second-order cone based approach to derive an exact convex formulation of the TRS, and under slightly stro...

This paper presents a real-time solution method of the maximum divert trajectory optimization problem for planetary landing. In mid-course, the vehicle is to abort and retarget to a landing site as far from the nominal as physically possible. The divert trajectory must satisfy velocity constraints in the range and cross range directions and a total speed constraint. The thrust magnitude is boun...