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Cheap Newton steps for optimal control problems: automatic differentiation and Pantoja's algorithm 最优控制问题的廉价牛顿步:自动微分和Pantoja算法
IF 2.2 3区 数学
Optimization Methods & Software Pub Date : 1999-01-01 DOI: 10.1080/10556789908805736
B. Christianson
{"title":"Cheap Newton steps for optimal control problems: automatic differentiation and Pantoja's algorithm","authors":"B. Christianson","doi":"10.1080/10556789908805736","DOIUrl":"https://doi.org/10.1080/10556789908805736","url":null,"abstract":"In this paper we discuss Pantoja's construction of the Newton direction for discrete time optimal control problems. We show that automatic differentiation (AD) techniques can be used to calculate the Newton direction accurately, without requiring extensive re-writing of user code, and at a surprisingly low computational cost: for an N-step problem with p control variables and q state variables at each step, the worst case cost is 6(p + q + 1) times the computational cost of a single target function evaluation, independent of N, together with at most p 3/3 + p 2(q + 1) + 2p(q + 1)2 + (q + l)3, i.e. less than (p + q + l)3, floating point multiply-and-add operations per time step. These costs may be considerably reduced if there is significant structural sparsity in the problem dynamics. The systematic use of checkpointing roughly doubles the operation counts, but reduces the total space cost to the order of 4pN floating point stores. A naive approach to finding the Newton step would require the solution of ...","PeriodicalId":54673,"journal":{"name":"Optimization Methods & Software","volume":"24 1","pages":"729-743"},"PeriodicalIF":2.2,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81428988","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: 18
Benchmarking interior point Lp/Qp solvers 对内点Lp/Qp求解器进行基准测试
IF 2.2 3区 数学
Optimization Methods & Software Pub Date : 1999-01-01 DOI: 10.1080/10556789908805767
H. Mittelmann
{"title":"Benchmarking interior point Lp/Qp solvers","authors":"H. Mittelmann","doi":"10.1080/10556789908805767","DOIUrl":"https://doi.org/10.1080/10556789908805767","url":null,"abstract":"In this work results of a comparison of five LP codes, BPMPD, HOPDM, LOQO, LIPSOL, and SOPLEX are reported and also of the first three as QP solvers. Since LOQO can solve general NLP problems it is in another class. For LP/QP problems it proves to be robust but it solves certain LP problems somewhat slower due to its limited presolve feature. SOPLEX as the only simplex-based program is highly competitive in general but is beaten by the best IPM codes on certain problems. Among the IPM codes BPMPD stands out while HOPDM has not been perfected as much for the solution of LP/QP problems but rather for use in other contexts requiring its pioneering warmstart feature which is now also available for BPMPD. LIPSOL is the only code in Matlab which has both advantages and disadvantages. It is a pure LP solver and has thus limited applicability compared to the other codes but solves LP problems with an efficiency close to that of BPMPD and HOPDM.","PeriodicalId":54673,"journal":{"name":"Optimization Methods & Software","volume":"72 1","pages":"655-670"},"PeriodicalIF":2.2,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84178135","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
CSDP 2.3 user's guide CSDP 2.3用户指南
IF 2.2 3区 数学
Optimization Methods & Software Pub Date : 1999-01-01 DOI: 10.1080/10556789908805764
B. Borchers
{"title":"CSDP 2.3 user's guide","authors":"B. Borchers","doi":"10.1080/10556789908805764","DOIUrl":"https://doi.org/10.1080/10556789908805764","url":null,"abstract":"The CSDP software package consists of a subroutine library for solving semidefinite programming problems, a stand alone solver for solving problems in the SDPA sparse format, some examples showing how to use CSDP, and utility programs for converting between SDPA sparse problem format and the SDPpack problem format. This user's guide describes how to install and use the software.","PeriodicalId":54673,"journal":{"name":"Optimization Methods & Software","volume":"64 1","pages":"597-611"},"PeriodicalIF":2.2,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85138622","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: 51
Computing the Combinatorial Canonical Form of a Layered Mixed Matrix 计算层状混合矩阵的组合标准形式
IF 2.2 3区 数学
Optimization Methods & Software Pub Date : 1998-04-01 DOI: 10.1080/10556789808805720
K. Murota, Mark Scharbrodt
{"title":"Computing the Combinatorial Canonical Form of a Layered Mixed Matrix","authors":"K. Murota, Mark Scharbrodt","doi":"10.1080/10556789808805720","DOIUrl":"https://doi.org/10.1080/10556789808805720","url":null,"abstract":"This paper presents an improved algorithm for computing the Combinatorial Canonical Form (CCF) of a layered mixed matrix which consists of a numerical matrix Q and a generic matrix T. The CCF is the (combinatorially unique) finest block-triangular form obtained by the row operations on the Q-part, followed by permutations of rows and columns of the whole matrix. The main ingredient of the improvements is the introduction of two precalculation phases. Computational results are also reported.","PeriodicalId":54673,"journal":{"name":"Optimization Methods & Software","volume":"13 1","pages":"373-391"},"PeriodicalIF":2.2,"publicationDate":"1998-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79026064","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: 1
Monotonicity of primal–dual interior-point algorithms for semidefinite programming problems 半定规划问题的原-对偶内点算法的单调性
IF 2.2 3区 数学
Optimization Methods & Software Pub Date : 1998-01-01 DOI: 10.1080/10556789808805715
M. Kojima, L. Tunçel
{"title":"Monotonicity of primal–dual interior-point algorithms for semidefinite programming problems","authors":"M. Kojima, L. Tunçel","doi":"10.1080/10556789808805715","DOIUrl":"https://doi.org/10.1080/10556789808805715","url":null,"abstract":"We present primal–dual interior-point algorithms with polynomial iteration bounds to find approximate solutions of semidefinite programming problems. Our algorithms achieve the current best iteration bounds and, in every iteration of our algorithms, primal and dual objective values are strictly improved.","PeriodicalId":54673,"journal":{"name":"Optimization Methods & Software","volume":"9 1","pages":"275-296"},"PeriodicalIF":2.2,"publicationDate":"1998-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76359632","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
Automatic differentiation and spectral projected gradient methods for optimal control problems 最优控制问题的自动微分和谱投影梯度方法
IF 2.2 3区 数学
Optimization Methods & Software Pub Date : 1998-01-01 DOI: 10.1080/10556789808805707
Ernesto G. Birgina, Yuri G. Evtusenko
{"title":"Automatic differentiation and spectral projected gradient methods for optimal control problems","authors":"Ernesto G. Birgina, Yuri G. Evtusenko","doi":"10.1080/10556789808805707","DOIUrl":"https://doi.org/10.1080/10556789808805707","url":null,"abstract":"Automatic differentiation and nonmonotone spectral projected gradient techniques are used for solving optimal control problems. The original problem is reduced to a nonlinear programming one using general Runge–Kutta integration formulas. Canonical formulas which use a fast automatic differentiation strategy are given to compute derivatives of the objective function. On the basis of this approach, codes for solving optimal control problems are developed and some numerical results are presented.","PeriodicalId":54673,"journal":{"name":"Optimization Methods & Software","volume":"21 1","pages":"125-146"},"PeriodicalIF":2.2,"publicationDate":"1998-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81549696","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: 32
Convergence rate of primal dual reciprocal Barrier Newton interior-point methods 原始对偶互易势垒牛顿内点法的收敛速度
IF 2.2 3区 数学
Optimization Methods & Software Pub Date : 1998-01-01 DOI: 10.1080/10556789808805685
A. El-Bakry
{"title":"Convergence rate of primal dual reciprocal Barrier Newton interior-point methods","authors":"A. El-Bakry","doi":"10.1080/10556789808805685","DOIUrl":"https://doi.org/10.1080/10556789808805685","url":null,"abstract":"Primal-dual interior-point methods for linear programming are often motivated by a certaijn nonlinear transformation of the Karush-Kuhn-Tucker conditions of the logarithmic Barrier formulation. Recently, Nassar [5] studied the reciprocal Barrier function formulation of the problem. Using a similar nonlinear transformation, he proved local convergence fir Newton interior-point method on the resulting perturbed Karush-Kuhn-Tucker systerp. This result poses the question whether this method can exhibit fast convergence ral[e for linear programming. In this paper we prove that, for linear programming, Newton's method on the reciprocal Barrier formulation exhibits at best Q-linear convergence rattf. Moreover, an exact Q1 factor is established which precludes fast linear convergence","PeriodicalId":54673,"journal":{"name":"Optimization Methods & Software","volume":"11 1","pages":"37-44"},"PeriodicalIF":2.2,"publicationDate":"1998-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84265661","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
On the convergence of combined relaxation methods for variational inequalties 变分不等式组合松弛方法的收敛性
IF 2.2 3区 数学
Optimization Methods & Software Pub Date : 1998-01-01 DOI: 10.1080/10556789808805687
I. Konnov
{"title":"On the convergence of combined relaxation methods for variational inequalties","authors":"I. Konnov","doi":"10.1080/10556789808805687","DOIUrl":"https://doi.org/10.1080/10556789808805687","url":null,"abstract":"A general approach to constructing iterative methods that solve variational inequaliti under mild assumptions is proposed. It is based on combining and modifying ide contained in various relaxation methods. The conditions under which the proposed metho attain linear convergence or terminate with a solution are also given","PeriodicalId":54673,"journal":{"name":"Optimization Methods & Software","volume":"43 1","pages":"77-92"},"PeriodicalIF":2.2,"publicationDate":"1998-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76836604","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: 7
Square grids with long “diagonals” 带有长“对角线”的方形网格
IF 2.2 3区 数学
Optimization Methods & Software Pub Date : 1998-01-01 DOI: 10.1080/10556789808805712
Z. Gáspár, N. Radics, A. Recski
{"title":"Square grids with long “diagonals”","authors":"Z. Gáspár, N. Radics, A. Recski","doi":"10.1080/10556789808805712","DOIUrl":"https://doi.org/10.1080/10556789808805712","url":null,"abstract":"Bolker and Crapo gave a graph theoretical model of square grid frameworks with diagonal rods of certain squares. Baglivo and Graver solved the problem of tensegrity frameworks where diagonal cables may be used in the square grid to make it rigid. The problem of one-story buildings in both cases can be reduced to the planar problems. These results are generalized if some longer rods, respectively some longer cables are also permitted.","PeriodicalId":54673,"journal":{"name":"Optimization Methods & Software","volume":"7 1","pages":"217-231"},"PeriodicalIF":2.2,"publicationDate":"1998-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81368699","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: 9
Computing a sparse Jacobian matrix by rows and columns 通过行和列计算稀疏雅可比矩阵
IF 2.2 3区 数学
Optimization Methods & Software Pub Date : 1998-01-01 DOI: 10.1080/10556789808805700
A. Hossain, T. Steihaug
{"title":"Computing a sparse Jacobian matrix by rows and columns","authors":"A. Hossain, T. Steihaug","doi":"10.1080/10556789808805700","DOIUrl":"https://doi.org/10.1080/10556789808805700","url":null,"abstract":"Efficient estimation of large sparse Jacobian matrices has been studied extensively in the last couple of years. It has been observed that the estimation of Jacobian matrix can be posed as a graph coloring problem. Elements of the matrix are estimated by taking divided difference in several directions corresponding to a group of structurally independent columns. Another possibility is to obtain the nonzero elements by means of the so called Automatic differentiation, which gives the estimates free of truncation error that one encounters in a divided difference scheme. In this paper we show that it is possible to exploit sparsity both in columns and rows by employing the forward and the reverse mode of Automatic differentiation. A graph-theoretic characterization of the problem is given.","PeriodicalId":54673,"journal":{"name":"Optimization Methods & Software","volume":"12 1","pages":"33-48"},"PeriodicalIF":2.2,"publicationDate":"1998-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87239737","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: 45
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