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

2019 ◽  
pp. 25-32
Keyword(s):  
Objective Function ◽  
Optimization Problem ◽  
Mathematical Optimization ◽  
Optimization Method ◽  
Optimal Location ◽  
Proximal Point Method ◽  
Localization Problem ◽  
Proximal Point ◽  
Localization Theory ◽  
Mathematical Optimization Problem

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.

scholarly journals Proximal point algorithm for differentiable quasi-convex multiobjective optimization

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2367-2376
Author(s):  
Fouzia Amir ◽  
Ali Farajzadeh ◽  
Narin Petrot
Keyword(s):  
Multiobjective Optimization ◽  
Objective Function ◽  
Critical Points ◽  
Proximal Point Algorithm ◽  
Optimization Problem ◽  
Proximal Point Method ◽  
Multiobjective Optimization Problem ◽  
Proximal Point ◽  
Accumulation Points ◽  
Locally Lipschitz

The main aim of this paper is to consider the proximal point method for solving multiobjective optimization problem under the differentiability, locally Lipschitz and quasi-convex conditions of the objective function. The control conditions to guarantee that the accumulation points of any generated sequence, are Pareto critical points are provided.

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

2020 ◽  
Vol 295 (1) ◽  
pp. 337-362
Author(s):  
Lars Schewe ◽  
Martin Schmidt ◽  
Johannes Thürauf
Keyword(s):  
Optimization Problem ◽  
Mathematical Optimization ◽  
Entry And Exit ◽  
Flow Models ◽  
Graph Classes ◽  
System Operator ◽  
Mathematical Optimization Problem ◽  
Market Organization ◽  
Gas Market

Abstract 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.

Minimum Vibration Cam Profiles

1968 ◽  
Vol 10 (3) ◽  
pp. 219-227 ◽  
Author(s):  
H. Kwakernaak ◽  
J. Smit
Keyword(s):  
Linear Programming ◽  
Optimization Problem ◽  
Numerical Solutions ◽  
Mathematical Optimization ◽  
Problem Formulation ◽  
Programming Formulation ◽  
Quadratic Problem ◽  
Linear Programming Formulation ◽  
Mathematical Optimization Problem ◽  
Minimal Residual

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.

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

1972 ◽  
Vol 1 (1) ◽  
pp. 31-36 ◽  
Author(s):  
F.Y. Chen ◽  
V.M. Dalsania
Keyword(s):  
Least Squares ◽  
Optimization Problem ◽  
Mathematical Optimization ◽  
Dimensional Synthesis ◽  
Gradient Search ◽  
Computer Solution ◽  
Numerical Examples ◽  
Function Generators ◽  
Mathematical Optimization Problem

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.

Research on the Shortest Path Problem Based on Green Transportation

2014 ◽  
Vol 1010-1012 ◽  
pp. 1858-1861
Author(s):  
Bao You Liu ◽  
Ya Ru Liu
Keyword(s):  
Shortest Path ◽  
Operations Research ◽  
Optimization Problem ◽  
Daily Life ◽  
Mathematical Optimization ◽  
Shortest Path Problem ◽  
Hebei Province ◽  
Research Knowledge ◽  
Green Transportation ◽  
Mathematical Optimization Problem

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.

scholarly journals Filled Function Method for Nonlinear Model Predictive Control

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Hajer Degachi ◽  
Bechir Naffeti ◽  
Wassila Chagra ◽  
Moufida Ksouri
Keyword(s):  
Objective Function ◽  
Predictive Control ◽  
Nonlinear Model ◽  
Nonconvex Optimization ◽  
Local Minimum ◽  
Optimization Problem ◽  
Optimization Method ◽  
Nonlinear Model Predictive Control ◽  
Hammerstein Model ◽  
Filled Function

A new method is used to solve the nonconvex optimization problem of the nonlinear model predictive control (NMPC) for Hammerstein model. Using nonlinear models in MPC leads to a nonlinear and nonconvex optimization problem. Since control performances depend essentially on the results of the optimization method, in this work, we propose to use the filled function as a global optimization method to solve the nonconvex optimization problem. Using this method, the control law can be obtained through two steps. The first step consists of determining a local minimum of the objective function. In the second step, a new function is constructed using the local minimum of the objective function found in the first step. The new function is called the filled function; the new constructed function allows us to obtain an initialization near the global minimum. Once this initialization is determined, we can use a local optimization method to determine the global control sequence. The efficiency of the proposed method is proved firstly through benchmark functions and then through the ball and beam system described by Hammerstein model. The results obtained by the presented method are compared with those of the genetic algorithm (GA) and the particle swarm optimization (PSO).

scholarly journals An improved 3DMax algorithm to reconstruct the three-dimensional structure of the chromosome

2020 ◽  
Author(s):  
Liwei Liu ◽  
Huili Yao
Keyword(s):  
Objective Function ◽  
Optimization Algorithm ◽  
Optimization Problem ◽  
3D Structure ◽  
Three Dimensional ◽  
Optimization Method ◽  
Dimensional Structure ◽  
Chromosome Conformation ◽  
Three Dimensional Structure ◽  
Interaction Map

AbstractIn recent years, with the development of high-throughput chromosome conformation capture (Hi-C) technology and the reduction of high-throughput sequencing cost, the data volume of whole-genome interaction has increased rapidly, and the resolution of interaction map keeps improving. Great progress has been made in the research of 3D structure modeling of chromosomes and genomes. Several methods have been proposed to construct the chromosome structure from chromosome conformation capture data. Based on the Hi-C data, this paper analyses the relevant literature of chromosome 3D structure reconstruction and it summarizes the principle of 3DMAX, which is a classical algorithm to construct the 3D structure of a chromosome. In this paper, we introduce a new gradient ascent optimization algorithm called XNadam that is a variant of Nadam optimization method. When XNadam is applied to 3DMax algorithm, the performance of 3DMax algorithm can be improved, which can be used to predict the three-dimensional structure of a chromosome.Author summaryThe exploration of the three-dimensional structure of chromosomes has gradually become a necessary means to understand the relationship between genome function and gene regulation. An important problem in the construction of three-dimensional model is how to use the interaction map. Usually, the interaction frequency can be transformed into the spatial distance according to the deterministic or non-deterministic function relationship, and the interaction frequency can be weighted as weight in the objective function of the optimization problem. When the frequency of interaction is weighted as weight in the objective function of the optimization problem, what kind of optimization method is used to optimize the objective function is the problem we consider. In order to solve this problem, we provide an improved stochastic gradient ascent optimization algorithm(XNadam). The XNadam optimization algorithm combined with maximum likelihood algorithm is applied to high resolution Hi-C data set to infer 3D chromosome structure.

Cavitating Flow Suppression for a Two-Phase Liquefied Natural Gas Expander Through Collaborative Fine-Turning Design Optimization of Impeller and Exducer Geometric Shape

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Peng Song ◽  
Jinju Sun ◽  
Changjiang Huo
Keyword(s):  
Natural Gas ◽  
Objective Function ◽  
Design Optimization ◽  
Optimization Problem ◽  
Optimization Method ◽  
Liquefied Natural Gas ◽  
Cavitating Flow ◽  
Two Phase ◽  
Phase Liquid ◽  
Adaptive Kriging

Abstract Cryogenic liquid turbine expanders have been increasingly used in liquefied natural gas (LNG) production plants to save energy. However, high-pressure LNG commonly needs to be throttled to or near a two-phase state, which makes the LNG turbine expander more vulnerable to cavitation. Although some work has been reported on cryogenic turbomachine cavitation, no work has been reported on designing a cavitation-resistant two-phase LNG liquid turbine expander. Motivated by the urgent requirement for two-phase liquid turbine expanders, an effective design optimization method is developed that is well-suited for designing the cavitation-resistant two-phase liquid turbine expanders. A novel optimization objective function is constituted by characterizing the cavitating flow, in which the overall efficiency and local cavitation flow behavior are incorporated. The adaptive-Kriging surrogate model and cooperative coevolutionary algorithm (CCEA) are incorporated to solve the highly nonlinear design optimization problem globally and efficiently. The former maintains high-level prediction accuracy of the objective function but uses much reduced computational fluid dynamics (CFD) simulations while the later solves the complex optimization problem at a high convergence rate through decomposing them into some readily solved parallel subproblems. By means of the developed optimization method, the impeller and exducer blade geometries and their axial gap and circumferential indexing are fine-tuned. Consequently, cavitating flow in both the impeller and exducer of the two-phase LNG expander is effectively mitigated.

Sign in / Sign up

Export Citation Format

Share Document