quadratic programming problems are widespread, class of nonlinear programmingproblems with many practical applications. The case of inequality constraints have been considered in a previous author's paper. In thi...
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(纸本)0780385470
quadratic programming problems are widespread, class of nonlinear programmingproblems with many practical applications. The case of inequality constraints have been considered in a previous author's paper. In this contribution an extension of these results for the case of inequality and equality constraints is presented. Based on equivalent formulation of Kuhn-Tucker conditions, a new neural network for solving the general quadratic programming problems, for the case of both inequality and equality constraints, is proposed. Two theorems for global stability and convergence of this network are given as well. The presented network has lower complexity for implementations and the. examples confirm its effectiveness. Simulation results based on SIMULINK (R) models are given and compared.
In this paper we present a relaxed version of an extragradient-proximal point algorithm recently proposed by Solodov and Svaiter for finding a zero of a maximal monotone operator defined on a Hilbert space. The aim is...
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In this paper we present a relaxed version of an extragradient-proximal point algorithm recently proposed by Solodov and Svaiter for finding a zero of a maximal monotone operator defined on a Hilbert space. The aim is to introduce a family of parameters in order to accelerate the rate of convergence of this algorithm. First we study the convergence and rate of convergence of the relaxed algorithms and then we apply them to the generalized variational inequality problem. For this problem, the operator is a sum of two operators: the first one is single-valued, monotone and continuous and the second one is the subdifferential of a nonsmooth lower semi-continuous proper convex function phi. To make the subproblems easier to solve, we consider, as in the bundle methods, piecewise linear convex approximations of phi. We explain how to construct these approximations and how the subproblems fall within the framework of our relaxed extragradient-proximal point algorithm. We prove the convergence of the resulting algorithm without assuming a Dunn property on the single-valued operator. Finally, we report some numerical experiences to illustrate the behavior of our implementable algorithm for different values of the relaxation factor. A comparison with another algorithm is also given.
In this paper, a neural network for quadratic programming problems is simplified. The simplicity is necessary for the high accuracy of solutions and low cost of implementation. The proposed network is proved to be an ...
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In this paper, a neural network for quadratic programming problems is simplified. The simplicity is necessary for the high accuracy of solutions and low cost of implementation. The proposed network is proved to be an extension of Newton's optimal descent flow about constraints problems and is globally convergent. The network dynamic behaviors are also discussed and these can get the feasible solution more easily. The simulations demonstrate the reasonability of the theory and advantages of the network. (C) 2001 Elsevier Science Inc. All rights reserved.
This paper presents a kind of dynamic genetic algorithm based on a continuous neural network, which is intrinsically the steepest decent method for constrained optimization problems. The proposed algorithm combines th...
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This paper presents a kind of dynamic genetic algorithm based on a continuous neural network, which is intrinsically the steepest decent method for constrained optimization problems. The proposed algorithm combines the local searching ability of the steepest decent methods with the global searching ability of genetic algorithms. Genetic algorithms are used to decide each initial point of the steepest decent methods so that all the initial points can be searched intelligently. The steepest decent methods are employed to decide the fitness of genetic algorithms so that some good initial points can be selected. The proposed algorithm is motivated theoretically and biologically. It can be used to solve a non-convex optimization problem which is quadratic and even more non-linear. Compared with standard genetic algorithms, it can improve the precision of the solution while decreasing the searching scale. In contrast to the ordinary steepest decent method, it can obtain global sub-optimal solution while lessening the complexity of calculation. (C) 2003 Elsevier Inc. All rights reserved.
In this paper the numerical stability of the orthogonal factorization method [5] for linear equality-constrained quadratic programming problems is studied using a backward error analysis. A perturbation formula for th...
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In this paper the numerical stability of the orthogonal factorization method [5] for linear equality-constrained quadratic programming problems is studied using a backward error analysis. A perturbation formula for the problem is analyzed;the condition numbers of this formula are examined in order to compare them with the condition numbers of the two matrices of the problem. A class of test problems is also considered in order to show experimentally the behaviour of the method.
Active-constraint logic for non-linear programming processes is sought such that the constraints in the active set possess positive projection multipliers and the resulting step does not violate the linear approximati...
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Active-constraint logic for non-linear programming processes is sought such that the constraints in the active set possess positive projection multipliers and the resulting step does not violate the linear approximations to any of the constraints satisfied as equalities but considered inactive. Active-constraint logic which has the desired properties is given for the cases of two and three constraints. For the general case featuring more than three constraints satisfied as equalities, an active-set logic is suggested. The efficiency of the proposed logic is tested computationally on some quadratic programming problems in comparison with three existing active-set strategies.
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