To ensure grid efficiency and reliability, powersystem operators continuously monitor the operational char-acteristics of the grid through a critical process called stateestimation (SE), which performs the task by filtering and fusingvarious measurements collected from grid sensors. This studyanalyzes the vulnerability of the key operation module, namelyAC-based SE, agai...

Many high dimensional data mining problems can be formulated as minimizing an empirical loss function with a penalty proportional to the number of variables required to describe a model. We propose a graduated non-convexification method to facilitate tracking of a global minimizer of this problem. We prove that under some conditions the proposed regularization problem using the continuous piece...

We consider sets defined by the usual stochastic ordering relation and by the second order stochastic dominance relation. Under fairy general assumptions we prove that in the space of integrable random variables the closed convex hull of the first set is equal to the second set.

Abstract Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations feasible set. Known approaches based on spatial branch-and-bound become more effective tighter used are. Relaxations are commonly established by underestimators, where each constraint fun...

We consider the design problem for a Marx generator electrical network, a pulsed power generator. The engineering specification of the design is that a suitable resonance condition is satisfied by the circuit so that the energy initially stored in a number of stage capacitors is transferred in finite time to a single load capacitor which can then store the total energy and deliver the pulse. We...

We propose a globally convergent numerical method, called the convexification, to numerically compute viscosity solution first-order Hamilton-Jacobi equations through vanishing process where parameter is fixed small number. By we mean that employ suitable Carleman weight function convexify cost functional defined directly from form of equation under consideration. The strict convexity this rigo...

Traditionally, most complex intelligence architectures are extremely non-convex, which could not be well performed by convex optimization. However, this paper decomposes complex structures into three types of nodes: operators, algorithms and functions. Further, iteratively propagating from node to node along edge, we prove that “regarding the neural graph without triangles, it is nearly convex ...