We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when t...
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We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology.
We describe an approach to the parallel and distributed solution of large-scale, block structured semidefinite programs using the spectral bundle method. Various elements of this approach (such as data distribution, a...
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We describe an approach to the parallel and distributed solution of large-scale, block structured semidefinite programs using the spectral bundle method. Various elements of this approach (such as data distribution, an implicitly restarted Lanczos method tailored to handle block diagonal structure, a mixed polyhedral-semidefinite subdifferential model, and other aspects related to parallelism) are combined in an implementation called LAMBDA, which delivers faster solution times than previously possible, and acceptable parallel scalability on sufficiently large problems.
In this paper, a nonlinear high-gain observer for the class of Lipschitz nonlinear systems is proposed. The proposed observer can be applied to multi-input-multi-output systems, without assuming any normal form repres...
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In this paper, a nonlinear high-gain observer for the class of Lipschitz nonlinear systems is proposed. The proposed observer can be applied to multi-input-multi-output systems, without assuming any normal form representation. The applicability of the proposed observer design to a given Lipschitz nonlinear system can be checked with the help of semidefinite programming (SDP). If the SDP has a solution, a nonlinear observer gain parameterized by the speed of the observer is obtained.
semidefinite programs (SDP) have been used in many recentapproximation algorithms. We develop a general primal-dualapproach to solve SDPs using a generalization ofthe well-known multiplicative weights update rule to s...
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ISBN:
(纸本)9781595936318
semidefinite programs (SDP) have been used in many recentapproximation algorithms. We develop a general primal-dualapproach to solve SDPs using a generalization ofthe well-known multiplicative weights update rule to symmetricmatrices. For a number of problems, such as Sparsest Cut and Balanced Separator in undirected and directed weighted graphs, and the Min UnCut problem, this yields combinatorial approximationalgorithms that are significantly more efficient than interiorpoint methods. The design of our primal-dual algorithms is guidedby a robust analysis of rounding algorithms used to obtain integersolutions from fractional ones.
The paper presents an efficient semidefinite programming (SDP) based design for prototype filters of cosine-modulated filter banks (CMFBs). We consider a class of near-perfect reconstruction CMFBs with the linear phas...
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ISBN:
(纸本)1424407281
The paper presents an efficient semidefinite programming (SDP) based design for prototype filters of cosine-modulated filter banks (CMFBs). We consider a class of near-perfect reconstruction CMFBs with the linear phase prototype filter, which structurally eliminates the amplitude overall distortion. The prototype filter design problem is then formulated into a convex semi-infinite programming problem. Furthermore, to handle the semi-infinite constraints, we use the linear matrix inequality (LMI) characterization of positive trigonometric polynomials to cast the semi-infinite programming problem into SDP one. Finally, convex duality is applied to transform the SDP into another SDP with the minimal number of additional variables, which is efficiently solved. An additional advantage of the proposed method is that we can precisely control the filter specifications.
In this paper, we propose a maximum separation margin (MSM) training method for multiple-prototype(MP)-based pattern classifiers in which a sample separation margin defined as the distance from the training-sample to ...
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ISBN:
(纸本)1424407281
In this paper, we propose a maximum separation margin (MSM) training method for multiple-prototype(MP)-based pattern classifiers in which a sample separation margin defined as the distance from the training-sample to the classification boundary can be calculated precisely. Similar to support vector machine (SVM) methodology, MSM training is formulated as a multicriteria optimization problem which aims at maximizing the separation margin and minimizing the empirical error rate on training data simultaneously. By making certain relaxation assumptions, MSM training can be reformulated as a semidefinite programming (SDP) problem that can be solved efficiently by some standard optimization algorithms designed for SDP. Evaluation experiments are conducted on the task of the recognition of most confusable Kanji character pairs identified from popular Nakayosi and Kuchibue handwritten Japanese character databases. It is observed that the MSM-trained MP-based classifier achieves a similar character recognition accuracy as that of the state-of-the-art SVM-based classifier, yet requires much fewer classifier parameters.
This paper proposes a novel method to design two-channel filter banks composed of exactly linear phase IIR filters. Broadly speaking, the design problem is formulated as a semidefinite program (SDP) of minimal order s...
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ISBN:
(纸本)9781424408818
This paper proposes a novel method to design two-channel filter banks composed of exactly linear phase IIR filters. Broadly speaking, the design problem is formulated as a semidefinite program (SDP) of minimal order such that the computational complexity is lower than that of existing, optimization-based method. Furthermore, it is more flexible than the maximally flat approach as various filter specifications can be easily incorporated. The applicability and efficiency of the proposed method is demonstrated through several numerical examples.
Lovasz and Schrijver (SIAM J. Optim. 1:166-190, 1991) have constructed semidefinite relaxations for the stable set polytope of a graph G = (V,E) by a sequence of lift-and-project operations;their procedure finds the s...
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ISBN:
(纸本)3540261990
Lovasz and Schrijver (SIAM J. Optim. 1:166-190, 1991) have constructed semidefinite relaxations for the stable set polytope of a graph G = (V,E) by a sequence of lift-and-project operations;their procedure finds the stable set polytope in at most alpha(G) steps, where alpha(G) is the stability number of G. Two other hierarchies of semidefinite bounds for the stability number have been proposed by Lasserre (SIAM J. Optim. 11:796-817, 2001;Lecture Notes in Computer Science, Springer, Berlin Heidelberg New York, pp 293-303, 2001) and by de Klerk and Pasechnik (SIAM J. Optim. 12:875-892), which are based on relaxing nonnegativity of a polynomial by requiring the existence of a sum of squares decomposition. The hierarchy of Lasserre is known to converge in alpha(G) steps as it refines the hierarchy of Lovasz and Schrijver, and de Klerk and Pasechnik conjecture that their hierarchy also finds the stability number after alpha(G) steps. We prove this conjecture for graphs with stability number at most 8 and we show that the hierarchy of Lasserre refines the hierarchy of de Klerk and Pasechnik.
We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when t...
详细信息
We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology.
Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within const...
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Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within constraint programming. In principle, we use the solution of a semidefinite relaxation to guide the traversal of the search tree, using a limited discrepancy search strategy. Furthermore, a semidefinite relaxation produces a bound for the solution value, which is used to prune parts of the search tree. Experimental results on stable set and maximum clique problem instances show that constraint programming can indeed greatly benefit from semidefinite relaxations. (c) 2005 Elsevier Ltd. All rights reserved.
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