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Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
This article is devoted to the study of certain models for phase transitions involving nonlocal energies. A first part is concerned with to the asymptotic analysis of a system of fractional elliptic equations of Allen-Cahn type as a…
We propose a linear programming (LP) framework for steady-state diffusion and flux optimization on geometric networks. The state variable satisfies a discrete diffusion law on a weighted, oriented graph, where conductances are scaled by…
Natural gas ranks second in consumption among primary energy sources in the United States. The majority of production sites are in remote locations, hence natural gas needs to be transported through a pipeline network equipped with a…
In this paper, we present a new approach to linearizing zero-one quadratic minimization problem which has many applications in computer science and communications. Our algorithm is based on the observation that the quadratic term of…
The quadratic cycle cover problem is the problem of finding a set of node-disjoint cycles visiting all the nodes such that the total sum of interaction costs between consecutive arcs is minimized. In this paper we study the linearization…
We develop a linear method for solving the nonlinear differential equations of a lumped-parameter thermal model of a spacecraft moving in a closed orbit. Our method, based on perturbation theory, is compared with heuristic linearizations of…
This paper proposes a component-based dual decomposition of the nonconvex AC optimal power flow (OPF) problem, where the modified dual function is solved in a distributed fashion. The main contribution of this work is that is demonstrates…
Linearization of power flow is an important topic in power system analysis. The computational burden can be greatly reduced under the linear power flow model while the model error is the main concern. Therefore, various linear power flow…
By generalizing the notion of linearization, a concept originally arising from microlocal analysis and symbolic calculus, to diffeological spaces, we make a first proposal setting for optimization problems in this category. We show how…
We formulate a general shape and topology optimization problem in structural optimization by using a phase field approach. This problem is considered in view of well-posedness and we derive optimality conditions. We relate the diffuse…
Transmission-constrained problems in power systems can be cast as polynomial optimization problems whose coefficients vary over time. We consider the complications therein and suggest several approaches. On the example of the…
Many problems in power systems involve optimizing a certain objective function subject to power flow equations and engineering constraints. A long-standing challenge in solving them is the nonconvexity of their feasible sets. In this paper,…
This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory…
The solution to an optimal power flow (OPF) problem provides a minimum cost operating point for an electric power system. The performance of OPF solution techniques strongly depends on the problem's feasible space. This paper presents an…
This paper considers distribution networks featuring inverter-interfaced distributed energy resources, and develops distributed feedback controllers that continuously drive the inverter output powers to solutions of AC optimal power flow…
Invariant linearization criteria of square systems of second-order quadratically semi-linear ordinary differential equations (ODEs) that can be represented as geodesic equations are extended to square systems of ODEs cubically nonlinear in…
As a representative mathematical expression of power flow (PF) constraints in electrical distribution system (EDS), the piecewise linearization (PWL) based PF constraints have been widely used in different EDS optimization scenarios.…
Optimal power flow (OPF) is considered for microgrids, with the objective of minimizing either the power distribution losses, or, the cost of power drawn from the substation and supplied by distributed generation (DG) units, while effecting…
Optimal power flow (OPF) is one of the most important optimization problems in the energy industry. In its simplest form, OPF attempts to find the optimal power that the generators within the grid have to produce to satisfy a given demand.…