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Initial values for Riccati ODEs from variational PDEs 由变分偏微分方程得到Riccati偏微分方程的初值
IF 2.6 3区 数学
Computational & Applied Mathematics Pub Date : 2011-07-18 DOI: 10.1590/S1807-03022011000200005
V. Costanza, P. Rivadeneira
{"title":"Initial values for Riccati ODEs from variational PDEs","authors":"V. Costanza, P. Rivadeneira","doi":"10.1590/S1807-03022011000200005","DOIUrl":"https://doi.org/10.1590/S1807-03022011000200005","url":null,"abstract":"The recently discovered variational PDEs (partial differential equations) for finding missing boundary conditions in Hamilton equations of optimal control are applied to the extended-space transformation of time-variant linear-quadratic regulator (LQR) problems. These problems become autonomous but with nonlinear dynamics and costs. The numerical solutions to the PDEs are checked against the analytical solutions to the original LQR problem. This is the first validation of the PDEs in the literature for a nonlinear context. It is also found that the initial value of the Riccati matrix can be obtained from the spatial derivative of the Hamiltonian flow, which satisfies the variational equation. This last result has practical implications when implementing two-degrees-of freedom control strategies for nonlinear systems with generalized costs.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2011-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73632567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
A universal constant for semistable limit cycles 半稳定极限环的一个通用常数
IF 2.6 3区 数学
Computational & Applied Mathematics Pub Date : 2011-07-18 DOI: 10.1590/S1807-03022011000200012
Joan C. Artés, J. Llibre, M. Teixeira
{"title":"A universal constant for semistable limit cycles","authors":"Joan C. Artés, J. Llibre, M. Teixeira","doi":"10.1590/S1807-03022011000200012","DOIUrl":"https://doi.org/10.1590/S1807-03022011000200012","url":null,"abstract":"We consider one-parameter families of 2-dimensional vector fields Xµ having in a convenient region R a semistable limit cycle of multiplicity 2m when µ = 0, no limit cycles if µ 0. We show, analytically for some particular families and numerically for others, that associated to the semistable limit cycle and for positive integers n sufficiently large there is a power law in the parameter µ of the form µn ≈ Cnα< 0 with C, α ∈ R, such that the orbit of Xµn through a point of p ∈ R reaches the position of the semistable limit cycle of X0 after given n turns. The exponent α of this power law depends only on the multiplicity of the semistable limit cycle, and is independent of the initial point p ∈ R and of the family Xµ. In fact α = -2m/(2m - 1). Moreover the constant C is independent of the initial point p ∈ R, but it depends on the family Xµ and on the multiplicity 2m of the limit cycle Γ.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2011-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80886888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Comparing stochastic optimization methods to solve the medium-term operation planning problem 比较随机优化方法解决中期运营计划问题
IF 2.6 3区 数学
Computational & Applied Mathematics Pub Date : 2011-07-18 DOI: 10.1590/S1807-03022011000200003
R. Gonçalves, E. Finardi, E. L. D. Silva, M. L. Santos
{"title":"Comparing stochastic optimization methods to solve the medium-term operation planning problem","authors":"R. Gonçalves, E. Finardi, E. L. D. Silva, M. L. Santos","doi":"10.1590/S1807-03022011000200003","DOIUrl":"https://doi.org/10.1590/S1807-03022011000200003","url":null,"abstract":"The Medium-Term Operation Planning (MTOP) of hydrothermal systems aims to define the generation for each power plant, minimizing the expected operating cost over the planning horizon. Mathematically, this task can be characterized as a linear, stochastic, large-scale problem which requires the application of suitable optimization tools. To solve this problem, this paper proposes to use the Nested Decomposition, frequently used to solve similar problems (as in Brazilian case), and Progressive Hedging, an alternative method, which has interesting features that make it promising to address this problem. To make a comparative analysis between these two methods with respect to the quality of the solution and the computational burden, a benchmark is established, which is obtained by solving a single Linear Programming problem (the Deterministic Equivalent Problem). An application considering a hydrothermal system is carried out.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2011-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90058556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
A study of axi-symmetric waves through an isotropic thermoelastic diffusive medium 通过各向同性热弹性扩散介质的轴对称波的研究
IF 2.6 3区 数学
Computational & Applied Mathematics Pub Date : 2011-07-18 DOI: 10.1590/S1807-03022011000200001
Rajesh Kumar, M. Panchal
{"title":"A study of axi-symmetric waves through an isotropic thermoelastic diffusive medium","authors":"Rajesh Kumar, M. Panchal","doi":"10.1590/S1807-03022011000200001","DOIUrl":"https://doi.org/10.1590/S1807-03022011000200001","url":null,"abstract":"The paper deals with the propagation of axial symmetric cylindrical surface waves in a cylindrical bore through a homogeneous isotropic thermoelastic diffusive medium of infinite extent. The three theories of thermoelasticity namely, Coupled Thermoelasticity (CT), Lord and Shulman (L-S) and Green and Lindsay (G-L) are used to study the problem. The frequency equations, connecting the phase velocity with wave number, radius of bore and other material parameters, for empty and liquid filled bore are derived. The numerical results obtained have been illustrated graphically to understand the behaviour of phase velocity and attenuation coefficient versus wave number of a wave. A particular case of interest has also been deduced from the present investigation.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2011-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80759145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A semi-analytical computation of the Kelvin kernel for potential flows with a free surface 自由表面势流开尔文核的半解析计算
IF 2.6 3区 数学
Computational & Applied Mathematics Pub Date : 2011-07-18 DOI: 10.1590/S1807-03022011000200002
J. D'Elía, L. Battaglia, Mario Alberto Storti
{"title":"A semi-analytical computation of the Kelvin kernel for potential flows with a free surface","authors":"J. D'Elía, L. Battaglia, Mario Alberto Storti","doi":"10.1590/S1807-03022011000200002","DOIUrl":"https://doi.org/10.1590/S1807-03022011000200002","url":null,"abstract":"A semi-analytical computation of the three dimensional Green function for seakeeping flow problems is proposed. A potential flow model is assumed with an harmonic dependence on time and a linearized free surface boundary condition. The multiplicative Green function is expressed as the product of a time part and a spatial one. The spatial part is known as the Kelvin kernel, which is the sum of two Rankine sources and a wave-like kernel, being the last one written using the Haskind-Havelock representation. Numerical efficiency is improved by an analytical integration of the two Rankine kernels and the use of a singularity subtractive technique for the Haskind-Havelock integral, where a globally adaptive quadrature is performed for the regular part and an analytic integration is used for the singular one. The proposed computation is employed in a low order panel method with flat triangular elements. As a numerical example, an oscillating floating unit hemisphere in heave and surge modes is considered, where analytical and semi-analytical solutions are taken as a reference.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2011-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79178083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 17
A family of uniformly accurate order Lobatto-Runge-Kutta collocation methods 一类均匀精确阶Lobatto-Runge-Kutta配置方法
IF 2.6 3区 数学
Computational & Applied Mathematics Pub Date : 2011-07-18 DOI: 10.1590/S1807-03022011000200004
D. G. Yakubu, N. Manjak, S. Buba, A. I. Maksha
{"title":"A family of uniformly accurate order Lobatto-Runge-Kutta collocation methods","authors":"D. G. Yakubu, N. Manjak, S. Buba, A. I. Maksha","doi":"10.1590/S1807-03022011000200004","DOIUrl":"https://doi.org/10.1590/S1807-03022011000200004","url":null,"abstract":"We consider the construction of an interpolant for use with Lobatto-Runge-Kutta collocation methods. The main aim is to derive single symmetric continuous solution(interpolant) for uniform accuracy at the step points as well as at the off-step points whose uniform order six everywhere in the interval of consideration. We evaluate the continuous scheme at different off-step points to obtain multi-hybrid schemes which if desired can be solved simultaneously for dense approximations. The multi-hybrid schemes obtained were converted to Lobatto-Runge-Kutta collocation methods for accurate solution of initial value problems. The unique feature of the paper is the idea of using all the set of off-step collocation points as additional interpolation points while symmetry is retained naturally by integration identities as equal areas under the various segments of the solution graph over the interval of consideration. We show two possible ways of implementing the interpolant to achieve the aim and compare them on some numerical examples.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2011-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81022500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Solving of time varying quadratic optimal control problems by using Bézier control points 利用bsamizier控制点求解时变二次型最优控制问题
IF 2.6 3区 数学
Computational & Applied Mathematics Pub Date : 2011-07-18 DOI: 10.1590/S1807-03022011000200007
M. Gachpazan
{"title":"Solving of time varying quadratic optimal control problems by using Bézier control points","authors":"M. Gachpazan","doi":"10.1590/S1807-03022011000200007","DOIUrl":"https://doi.org/10.1590/S1807-03022011000200007","url":null,"abstract":"In this paper, linear quadratic optial control probles are solved by applying least square method based on Bezier control points. We divide the interval which includes t, into k subintervals and approximate the trajectory and control functions by Bezier curves. We have chosen the Bezier curves as piacewise polynomials of degree three, and determined Bezier curves on any subinterval by four control points. By using least square ethod, e introduce an optimization problem and compute the control points by solving this optimization problem. Numerical experiments are presented to illustrate the proposed method.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2011-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78583953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 20
An inexact subgradient algorithm for Equilibrium Problems 平衡问题的非精确次梯度算法
IF 2.6 3区 数学
Computational & Applied Mathematics Pub Date : 2011-01-17 DOI: 10.1590/S1807-03022011000100005
P. J. S. Santos, S. Scheimberg
{"title":"An inexact subgradient algorithm for Equilibrium Problems","authors":"P. J. S. Santos, S. Scheimberg","doi":"10.1590/S1807-03022011000100005","DOIUrl":"https://doi.org/10.1590/S1807-03022011000100005","url":null,"abstract":"We present an inexact subgradient projection type method for solving a nonsmooth Equilibrium Problem in a finite-dimensional space. The proposed algorithm has a low computational cost per iteration. Some numerical results are reported.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2011-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74171692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 150
Derivative-free methods for nonlinear programming with general lower-level constraints 具有一般低级约束的非线性规划的无导数方法
IF 2.6 3区 数学
Computational & Applied Mathematics Pub Date : 2011-01-17 DOI: 10.1590/S1807-03022011000100003
M. A. Diniz-Ehrhardt, J. Martínez, L. G. Pedroso
{"title":"Derivative-free methods for nonlinear programming with general lower-level constraints","authors":"M. A. Diniz-Ehrhardt, J. Martínez, L. G. Pedroso","doi":"10.1590/S1807-03022011000100003","DOIUrl":"https://doi.org/10.1590/S1807-03022011000100003","url":null,"abstract":"Augmented Lagrangian methods for derivative-free continuous optimization with constraints are introduced in this paper. The algorithms inherit the convergence results obtained by Andreani, Birgin, Martinez and Schuverdt for the case in which analytic derivatives exist and are available. In particular, feasible limit points satisfy KKT conditions under the Constant Positive Linear Dependence (CPLD) constraint qualification. The form of our main algorithm allows us to employ well established derivative-free subalgorithms for solving lower-level constrained subproblems. Numerical experiments are presented.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2011-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81624242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 43
Two derivative-free methods for solving underdetermined nonlinear systems of equations 求解欠定非线性方程组的两种无导数方法
IF 2.6 3区 数学
Computational & Applied Mathematics Pub Date : 2011-01-01 DOI: 10.1590/S1807-03022011000100011
N. Echebest, M. L. Schuverdt, R. Vignau
{"title":"Two derivative-free methods for solving underdetermined nonlinear systems of equations","authors":"N. Echebest, M. L. Schuverdt, R. Vignau","doi":"10.1590/S1807-03022011000100011","DOIUrl":"https://doi.org/10.1590/S1807-03022011000100011","url":null,"abstract":"In this paper, two different approaches to solve underdetermined nonlinear system of equations are proposed. In one of them, the derivative-free method defined by La Cruz, Martinez and Raydan for solving square nonlinear systems is modified and extended to cope with the underdetermined case. The other approach is a Quasi-Newton method that uses the Broyden update formula and the globalized line search that combines the strategy of Grippo, Lampariello and Lucidi with the Li and Fukushima one. Global convergence results for both methods are proved and numerical experiments are presented.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74765214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
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