Computing technical capacities in the European entry-exit gas market is NP-hard

As a result of its liberalization, the European gas market is organized as an entry-exit system in order to decouple the trading and transport of natural gas. Roughly summarized, the gas market organization consists of four subsequent stages. First, the transmission system operator (TSO) is obliged to allocate so-called maximal technical capacities for the nodes of the network. Second, the TSO and the gas traders sign mid- to long-term capacity-right contracts, where the capacity is bounded above by the allocated technical capacities. These contracts are called bookings. Third, on a day-ahead basis, gas traders can nominate the amount of gas that they inject or withdraw from the network at entry and exit nodes, where the nominated amount is bounded above by the respective booking. Fourth and finally, the TSO has to operate the network such that the nominated amounts of gas can be transported. By signing the booking contract, the TSO guarantees that all possibly resulting nominations can indeed be transported. Consequently, maximal technical capacities have to satisfy that all nominations that comply with these technical capacities can be transported through the network. This leads to a highly challenging mathematical optimization problem. We consider the specific instantiations of this problem in which we assume capacitated linear as well as potential-based flow models. In this contribution, we formally introduce the problem of () and prove that it is -complete on trees and -hard in general. To this end, we first reduce the problem to for the case of capacitated linear flows in trees. Afterward, we extend this result to with potential-based flows and show that this problem is also -complete on trees by reducing it to the case of capacitated linear flow. Since the hardness results are obtained for the easiest case, i.e., on tree-shaped networks with capacitated linear as well as potential-based flows, this implies the hardness of for more general graph classes.

Novelty of Frequency Domain Data in Smart Structures using μ-Analysis

This paper deals with the advantages of robust control in smart structures. First we present the implementations of H infinity control in the frequency domain. A dynamic model for smart structure under wind excitations is considered. Then robust control theory is used a model to synthesize controllers achieving stabilization with guaranteed performance for smart structures. We use μ-analysis to express the control problem as a mathematical optimization problem and then find the controller that solves the optimization problem in the frequency domain.

Un Método de Optimización Proximal para Problemas de Localización Cuasi-convexa

Un Método de Optimización Proximal para Problemas de Localización Cuasi-convexa Miguel A. Cano Lengua, Erik A. Papa Quiroz Facultad de Ciencias Naturales y Matemática -FCNM/ Universidad Nacional del Callao Callao- Perú DOI: https://doi.org/10.33017/RevECIPeru2011.0018/ RESUMEN El problema de localización es de gran interés para poder establecer de manera óptima diferentes demandas de ubicación en el sector estatal o privado. El modelo de este problema se reduce generalmente a un problema de optimización matemática. En el presente trabajo presentamos un método de optimización proximal para resolver problemas de localización donde la función objetivo es cuasi-convexa y no diferenciable. Probamos que las iteraciones dadas por el método están bien definidas y bajo algunas hipótesis sobre la función objetivo probamos la convergencia del método. Descriptores: Método del punto proximal, teoría de localización, convergencia global, función cuasi-convexa. ABSTRACT The localization problem is of great interest to establish the optimal location of the different demands in the state or private sector. The model of this problem is generally reduced to solve a mathematical optimization problem. In the present work we present a proximal optimization method to solve localization problems where the objective function is non differentiable and quasiconvex. We prove that the iterations of the method are well defined and under some assumption on the objective function we prove the convergence of the method. Keywords: Proximal point method, localization theory, global convergence, quasiconvex function.

Research on the Shortest Path Problem Based on Green Transportation

The shortest path problem is a typical mathematical optimization problem which often encountered in the production field and daily life. From the perspective of green transportation, in this paper, the shortest path problem in Hebei Province was put forward that applied the operations research knowledge, and solved the analysis by lingo11.0. The results showed that the shortest path is 2230.00 km that started from Shijiazhuang through each prefecture-level city, then back to Shijiazhuang. The shortest path from Shijiazhuang to Qinhuangdao is 589.00 km.

Optimal Sythesis of Planar Six-Link Chains Using Least-Squares Gradient Search

The approximate dimensional synthesis of three basic forms of the planar six-link chain as function generators is formulated as a mathematical optimization problem. Least-squares gradient search scheme is used for the computer solution. Numerical examples are given.

Minimum Vibration Cam Profiles

The problem of finding cam profiles with limited follower velocity, acceleration and jerk and minimal residual vibrations over a prescribed range of cam speeds is formulated as a mathematical optimization problem. Two versions of the problem are considered: a quadratic problem formulation and a linear programming formulation. Numerical solutions have been found through the use of a digital computer and the methods are compared. Examples of profiles are presented which compare favourably with the well-known cycloidal profile.