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29th International Conference on Neural Information Processing

作者： Galkowski, Tomasz Krzyzak, Adam Czestochowa Tech Univ Inst Computat Intelligence Armii Krajowej 36 Czestochowa Poland Concordia Univ Dept Comp Sci & Software Engn Montreal PQ H3G 1M8 Canada Westpomeranian Univ Technol Dept Elect Engn Sikorskiego 37 PL-70313 Szczecin Poland

ISBN: (纸本)9789819916382;9789819916399

Various methods for estimation of unknown functions from the set of noisy measurements are applicable to a wide variety of problems. Among them the non-parametric algorithms based on the Parzen kernel are commonly used. Our method is basically developed for multidimensional case. The two-dimensional version of the method is thoroughly explained and analysed. The proposed algorithm is an effective and efficient solution significantly improving computational speed. Computational complexity and speed of convergence of the algorithm are also studied. Some applications for solving real problems with our algorithms are presented. Our approach is applicable to multidimensional regression function estimation as well as to estimation of derivatives of functions. It is worth noticing that the presented algorithms have already been used successfully in various image processing applications, achieving significant accelerations of calculations.

关键词： Parzen kernel algorithms nonparametric regression estimation multidimensional functions

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A version of Turan's problem for positive definite functions of several variables

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PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS 2012年第1-sup期277卷 93-112页

作者： Efimov, A. V. Ural Fed Univ Inst Math & Comp Sci Ekaterinburg 620083 Russia

Let be the class of functions of m variables with support in the unit ball centered at the origin of the space a"e (m) , continuous in a"e (m) , normed by the condition f(0) = 1, and having a nonnegative Fourier transform. In this paper, we study the problem of finding the maximum value I broken vertical bar (m) (a) of normed integrals of functions from the class over the sphere of radius a, 0 < a < 1, centered at the origin. It is proved that, in this problem, we may restrict our attention to spherically symmetric functions from . The existence of an extremal function is proved and a representation of this function as the self-convolution of a radial function is obtained. An integral equation is written for a solution of the problem for any m a parts per thousand yen 3. The values I broken vertical bar(3)(a) are calculated for 1/3 a parts per thousand currency sign a < 1.

关键词： Turan's problem positive definite functions multidimensional functions

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A computational analysis of multidimensional piecewise-linear models with applications to oil production optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2014年第3期232卷 630-642页

作者： Silva, Thiago Lima Camponogara, Eduardo Univ Fed Santa Catarina Dept Automat & Syst Engn BR-88040900 Florianopolis SC Brazil

Production optimization of gas-lifted oil wells under facility, routing and pressure constraints is a challenging problem, which has attracted the interest of operations engineers aiming to drive economic gains and scientists for its inherent complexity. The hardness of this problem rests on the non-linear characteristics of the multidimensional well-production and pressure-drop functions, as well as the discrete routing decisions. To this end, this work develops several formulations in Mixed-Integer Linear Programming (MILP) using multidimensional piecewise-linear models to approximate the non-linear functions with domains spliced in hypercubes and simplexes. Computational and simulation analyses were performed considering a synthetic but realistic oil field modeled with a multiphase-flow simulator. The purpose of the analyses was to assess the relative performance of the MILP formulations and their impact on the simulated oil production. (C) 2013 Elsevier B.V. All rights reserved.

关键词： OR in energy Integer programming multidimensional functions Piecewise linearization Oil production Pressure constraints

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An Improved Particle Swarm Optimization Algorithm for Global multidimensional Optimization

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JOURNAL OF INTELLIGENT SYSTEMS 2020年第1期29卷 127-142页

作者： Fair, Rkia Bouroumi, Abdelaziz Hassan II Univ Casablanca Ben Msik Fac Sci Informat Proc Lab Ave Driss El HartiBP 7955 Casablanca Morocco

This paper introduces a new variant of the particle swarm optimization (PSO) algorithm, designed for global optimization of multidimensional functions. The goal of this variant, called ImPSO, is to improve the exploration and exploitation abilities of the algorithm by introducing a new operation in the iterative search process. The use of this operation is governed by a stochastic rule that ensures either the exploration of new regions of the search space or the exploitation of good intermediate solutions. The proposed method is inspired by collaborative human learning and uses as a starting point a basic PSO variant with constriction factor and velocity clamping. Simulation results that show the ability of ImPSO to locate the global optima of multidimensional functions are presented for 10 well-know benchmark functions from CEC-2013 and CEC-2005. These results are compared with the PSO variant used as starting point, three other PSO variants, one of which is based on human learning strategies, and three alternative evolutionary computing methods.

关键词： Particle swarm optimization swarm intelligence global optimization multidimensional functions collaborative learning

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ON A CLASS OF GLOBAL OPTIMIZATION TEST functions

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NEURAL NETWORK WORLD 2009年第2期19卷 247-252页

作者： Grosan, Crina Abraham, Ajith Sci Network Innovat & Res Excellence MIR Labs Auburn WA 98071 USA Univ Babes Bolyai Dept Comp Sci R-3400 Cluj Napoca Romania

This paper provides a theoretical proof illustrating that for a certain class of functions having the property that the partial derivatives have the same equation with respect to all variables, the optimum value (minimum or maximum) takes place at a point where all the variables have the same value. This information will help the researchers working with high dimensional functions to minimize the computational burden due to the fact that the search has to be performed only with respect to one variable.

关键词： multidimensional functions global optimization first partial derivatives

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A radial focus+context visualization for multi-dimensional functions 02

A radial focus+context visualization for multi-dimensional f...

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Proceedings of the conference on Visualization '02

作者： Sanjini Jayaraman Chris North Virginia Polytechnic Institute and State University Blacksburg VA

ISBN: (纸本)9780780374980

The analysis of multidimensional functions is important in many engineering disciplines, and poses a major problem as the number of dimensions increases. Previous visualization approaches focus on representing three or fewer dimensions at a time. This paper presents a new focus+context visualization that provides an integrated overview of an entire multidimensional function space, with uniform treatment of all dimensions. The overview is displayed with respect to a user-controlled polar focal point in the function's parameter space. Function value patterns are viewed along rays that emanate from the focal point in all directions in the parameter space, and represented radially around the focal point in the visualization. Data near the focal point receives proportionally more screen space than distant data. This approach scales smoothly from two dimensions to 10-20, with a 1000 pixel range on each dimension.

关键词： visualization multidimensional functions

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