Related papers: On linear relaxations of OPF problems
The optimal power flow (OPF) problem seeks to control power generation/demand to optimize certain objectives such as minimizing the generation cost or power loss in the network. It is becoming increasingly important for distribution…
With increasing share of renewables in power generation mix, system operators would need to run Optimal Power Flow (OPF) problems closer to real-time to better manage uncertainty. Given that OPF is an expensive optimization problem to…
Optimal power flow (OPF) is an important problem in the operation of electric power systems. Due to the OPF problem's non-convexity, there may exist multiple local optima. Certifiably obtaining the global solution is important for certain…
By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…
This paper proposes a bilevel hierarchy of strengthened complex moment relaxations for complex polynomial optimization. The key trick entails considering a class of positive semidefinite conditions that arise naturally in characterizing the…
We get fractional symmetric Fokker - Planck and Einstein - Smoluchowski kinetic equations, which describe evolution of the systems influenced by stochastic forces distributed with stable probability laws. These equations generalize known…
The nonlinear programming (NLP) problem to solve distribution-level optimal power flow (D-OPF) poses convergence issues and does not scale well for unbalanced distribution systems. The existing scalable D-OPF algorithms either use…
The Optimal Power Flow (OPF) problem can be reformulated as a nonconvex Quadratically Constrained Quadratic Program (QCQP). There is a growing body of work on the use of semidefinite programming relaxations to solve OPF. The relaxation is…
Lifting methods allow to transform hard variational problems such as segmentation and optical flow estimation into convex problems in a suitable higher-dimensional space. The lifted models can then be efficiently solved to a global optimum,…
Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient…
We consider using particle production as a friction force by which to implement a "Relaxion" solution to the electroweak hierarchy problem. Using this approach, we are able to avoid superplanckian field excursions and avoid any conflict…
We establish derivative estimates of solution of elliptic system in narrow regions.
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…
We investigate hypergraphic LP relaxations for the Steiner tree problem, primarily the partition LP relaxation introduced by Koenemann et al. [Math. Programming, 2009]. Specifically, we are interested in proving upper bounds on the…
We consider the homogenized linear feasibility problem, to find an $x$ on the unit sphere, satisfying $n$ line ar inequalities $a_i^Tx\ge 0$. To solve this problem we consider the centers of the insphere of spherical simpl ices, whose…
An existing solvability result for relaxed one-sided Lipschitz algebraic inclusions is substantially improved. This enhanced solvability result allows the design of a very robust numerical method for the approximation of a solution of the…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
New estimates on the maximal function associated to the linear Schrodinger equation are established
In this paper we study the existence of solutions to an isotropic differential inclusion.