Related papers: ILP formulations for the two-stage stochastic Stei…
We compute time-dependent solutions of the sharp-interface model of dendritic solidification in two dimensions by using a level set method. The steady-state results are in agreement with solvability theory. Solutions obtained from the level…
Instanton theory is an established method to calculate rate constants of chemical reactions including atom tunneling. Technical and methodological improvements increased its applicability. Still, a large number of energy and gradient…
This paper proposes a reformulation of the scenario-based two-stage unit commitment problem under uncertainty that allows finding unit-commitment plans that perform reasonably well both in expectation and for the worst case realization of…
In this chapter, an integer linear programming formulation for the problem of obtaining task-relevant, multi-resolution, environment abstractions for resource-constrained autonomous agents is presented. The formulation leverages concepts…
We survey and compare, mainly in the two-dimensional case, various results obtained by IST and PDE techniques for integrable equations. We also comment on what can be predicted from integrable equations on non integrable ones.
In this paper a time dependent Stokes problem that is motivated by a standard sharp interface model for the fluid dynamics of two-phase flows is studied. This Stokes interface problem has discontinuous density and viscosity coefficients and…
We present a new multilevel method for calculating Poisson's equation, which often arises form electrostatic problems, by using hierarchical loop bases. This method, termed hierarchical Loop basis Poisson Solver (hieLPS), extends previous…
This paper provides an optimized cable path planning solution for a tree-topology network in an irregular 2D manifold in a 3D Euclidean space, with an application to the planning of submarine cable networks. Our solution method is based on…
In this paper we study the computational complexity of solving a class of block structured integer programs (IPs) - so called multistage stochastic IPs. A multistage stochastic IP is an IP of the form $\max \{ c^T x \mid \mathcal{A} x = b,…
The spinor-helicity formalism has proven to be very efficient in the calculation of scattering amplitudes in quantum field theory, while the loop tree duality (LTD) representation of multi-loop integrals exhibits appealing and interesting…
This paper proposes a Separable Projective Approximation Routine-Optimal Power Flow (SPAR-OPF) framework for solving two-stage stochastic optimization problems in power systems. The framework utilizes a separable piecewise linear…
In order to further enhance the computational efficiency of the implicit unified gas-kinetic scheme (IUGKS, JCP 315 (2016) 16-38) for multi-scale flow simulation, a two-step IUGKS is proposed in this paper. The multiscale solution of the…
Strong existence and pathwise uniqueness of solutions with $L^{\infty}$-vorticity of 2D stochastic Euler equations is proved. The noise is multiplicative and involves first derivatives. A Lagrangian approach is implemented, where a…
We introduce the fastest known exact algorithm~for~the multiterminal cut problem with k terminals. In particular, we engineer existing as well as new data reduction rules. We use the rules within a branch-and-reduce framework and to boost…
We study the Weighted Tree Augmentation Problem for general link costs. We show that the integrality gap of the ODD-LP relaxation for the (weighted) Tree Augmentation Problem for a $k$-level tree instance is at most $2 - \frac{1}{2^{k-1}}$.…
We present an algorithm for a class of $n$-fold ILPs: whose existing algorithms in literature typically (1) are based on the \textit{augmentation framework} where one starts with an arbitrary solution and then iteratively moves towards an…
We propose a new algorithm for solving multistage stochastic mixed integer linear programming (MILP) problems with complete continuous recourse. In a similar way to cutting plane methods, we construct nonlinear Lipschitz cuts to build lower…
A two-stage stochastic optimization model for the design of the closed-loop cable layout of an Offshore Wind Farm (OWF) is presented. The model consists on a Mixed Integer Linear Program (MILP) with scenario numeration incorporation to…
A general theory of stochastic extensive forms is developed to bridge two concepts of information flow: decision trees and refined partitions on the one side, filtrations from probability theory on the other. Instead of the traditional…
In this paper, we consider the scenario-based two-stage stochastic DC optimal power flow (OPF) problem for optimal and reliable dispatch when the load is facing uncertainty. Although this problem is a linear program, it remains…