An ε-subgradient projection algorithm for solving a convex feasibility problem is *** on the iterative projection methods and the notion of ε-subgradient,a series of special projection hyperplanes is ***,compared wi...
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An ε-subgradient projection algorithm for solving a convex feasibility problem is *** on the iterative projection methods and the notion of ε-subgradient,a series of special projection hyperplanes is ***,compared with the existing projection hyperplanes methods with subgradient,the proposed hyperplanes are interactive with ε,and their ranges are more *** convergence of the proposed algorithm is given under some mild conditions,and the validity of the algorithm is proved by the numerical test.
This paper proposes a projection algorithm which can be employed to bound actuator signals, in terms of both magnitude and rate, for uncertain systems with redundant actuators. The investigated closed-loop control sys...
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This paper proposes a projection algorithm which can be employed to bound actuator signals, in terms of both magnitude and rate, for uncertain systems with redundant actuators. The investigated closed-loop control system is assumed to contain an adaptive control allocator to distribute the total control input among actuators. Although conventional control allocation methods can handle actuator rate and magnitude constraints, they cannot consider actuator uncertainty. On the other hand, adaptive allocators manage uncertainty and actuator magnitude limits. The proposed projection algorithm enables adaptive control allocators to handle both magnitude and rate saturation constraints. A mathematically rigorous analysis is provided to show that with the help of the proposed projection algorithm, the performance of the adaptive control allocator can be guaranteed, in terms of error bounds. Simulation results are presented, where the Aero-Data Model In Research Environment (ADMIRE) is used to demonstrate the effectiveness of the proposed method.
We present a modification of a double projection algorithm proposed by Solodov and Svaiter for solving variational inequalities. The main modification is to use a different Armijo-type linesearch to obtain a hyperplan...
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We present a modification of a double projection algorithm proposed by Solodov and Svaiter for solving variational inequalities. The main modification is to use a different Armijo-type linesearch to obtain a hyperplane strictly separating current iterate from the solutions of the variational inequalities. Our method is proven to be globally convergent under very mild assumptions. If in addition a certain error bound holds, we analyze the convergence rate of the iterative sequence. We use numerical experiments to compare our method with that proposed by Solodov and Svaiter. (c) 2005 Elsevier B.V. All rights reserved.
The Convex Inequality Problem (CIP), i.e., find x is an element of R-n such that Ax = b, g(x) less than or equal to 0, where A is an p x n matrix, b is an element of R-m and g(.) : R-n --> R-m is a convex function,...
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The Convex Inequality Problem (CIP), i.e., find x is an element of R-n such that Ax = b, g(x) less than or equal to 0, where A is an p x n matrix, b is an element of R-m and g(.) : R-n --> R-m is a convex function, has been solved by projection algorithms possessing a linear rate of convergence. We propose a projection algorithm that exhibits global and superlinear rate of convergence under reasonable assumptions. Convergence is ensured if the CIP is not empty. A direction of search is found by solving a quadratic programming problem (the projection step). As opposed to previous algorithms no special stepsize procedure is necessary to ensure a superlinear rate of convergence. We suggest a possible application of this algorithm for solving convex constrained Linear Complementarity Problems, i.e., find x is an element of R-n such that x greater than or equal to 0, Ax + b greater than or equal to 0, [x, Ax + b] = 0, g(x) less than or equal to 0. A is an n x n positive semidefinite matrix and g(.) : R-n --> R-m is a convex function. (C) 1998 Elsevier Science B.V. All rights reserved.
In real life, data often appear in the form of sequences and this form of data is called sequence data. In this paper, a new definition on sequence similarity and a novel algorithm, projection algorithm, for sequence ...
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In real life, data often appear in the form of sequences and this form of data is called sequence data. In this paper, a new definition on sequence similarity and a novel algorithm, projection algorithm, for sequence data searching are proposed. This algorithm is not required to access every datum in a sequence database. However, it guarantees that no qualified subsequence is falsely rejected. Moreover, the projection algorithm can be extended to match subsequences with different scales. With careful selection of parameters, most of the similar subsequences with different scales can be retrieved. We also show by experiments that the proposed algorithm can outperform the traditional sequential searching algorithm up to 96 times in terms of speed up. (C) 1998 Elsevier Science B.V. All rights reserved.
In this paper, a derivative-free spectral projection technique to solve a system of large-scale nonlinear monotone equations is presented. The primary motivation is to use the appropriate structure of spectral conjuga...
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In this paper, a derivative-free spectral projection technique to solve a system of large-scale nonlinear monotone equations is presented. The primary motivation is to use the appropriate structure of spectral conjugate gradient directions in the projection algorithms. The new direction is derivative-free and requires a little storage and computation. So, it is an appropriate direction to use in large-scale projection algorithms. We prove the global convergence and R-linear convergence rate of the proposed algorithm under some suitable conditions. Numerical experiments show a promising behaviour of the proposed algorithm to deal with large-scale monotone equations. Additionally, as a practical application, we use the new method to solve the l(1)-norm regularization problems to reconstruct a sparse signal in compressed sensing.
In this paper, we propose a hybrid CQ projection algorithm with two projection steps and one Armijo-type line-search step for the split feasibility problem. The line-search technique is intended to construct a hyperpl...
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In this paper, we propose a hybrid CQ projection algorithm with two projection steps and one Armijo-type line-search step for the split feasibility problem. The line-search technique is intended to construct a hyperplane that strictly separates the current point from the solution set. The next iteration is obtained by the projection of the initial point on a regress region (the intersection of three sets). Hence, algorithm converges faster than some other algorithms. Under some mild conditions, we show the convergence. Preliminary numerical experiments show that our algorithm is efficient.
In this paper, we improve the convergence theorem in the paper by Yang (Journal of Industrial and Management Optimization 1, 211-217, 2005), and propose a new modified convergence theorem. The theorem and the proof pr...
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In this paper, we improve the convergence theorem in the paper by Yang (Journal of Industrial and Management Optimization 1, 211-217, 2005), and propose a new modified convergence theorem. The theorem and the proof presented in the present paper are interesting improvements on the convergence theorem of Yang.
Let E be a uniformly convex and uniformly smooth Banach space, let C be a nonempty closed convex subset of E, let {T-n} : C -> C be a countable family of weak relatively nonexpansive mappings such that F = boolean ...
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Let E be a uniformly convex and uniformly smooth Banach space, let C be a nonempty closed convex subset of E, let {T-n} : C -> C be a countable family of weak relatively nonexpansive mappings such that F = boolean AND(infinity)(n=1) F(T-n) not equal emptyset. For any given gauss x(0) is an element of C, define a sequence {x(n)} in C by the following algorithm: {C-0 = C, Cn+1 = {z is an element of C-n : phi(z, T(n)x(n)) = phi(z,x(n))}, n = 0,1,2,3,..., x(n+1) = Pi C(n+1)x(0). Then {x(n)} converges strongly to q = Pi(F)x(0).
To locate the spots in microarray images automatically, we combine the projection algorithm with statistic theory, making the gridding without absence and redundancy. The radius of spots could be estimated based on th...
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ISBN:
(纸本)9781424447138
To locate the spots in microarray images automatically, we combine the projection algorithm with statistic theory, making the gridding without absence and redundancy. The radius of spots could be estimated based on the improved algorithm, which is an important parameter in segmentation. Adaptive threshold is used to segment the image, and disk template generated automatically is used to detect the spots. The positive and weak spots could be detected correctly, so the methods are not only for the ideal images, but also for the images with many negative spots.
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