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Tsung-Min Hwang Chih-Hung Lin Wen-Wei Lin Shu-Cherng Fang 《Annals of Operations Research》1996,62(1):173-196
In this paper, we provide an easily satisfied relaxation condition for the primaldual interior path-following algorithm to solve linear programming problems. It is shown that the relaxed algorithm preserves the property of polynomial-time convergence. The computational results obtained by implementing two versions of the relaxed algorithm with slight modifications clearly demonstrate the potential in reducing computational efforts.Partially supported by the North Carolina Supercomputing Center, the 1993 Cray Research Award, and a National Science Council Research Grant of the Republic of China. 相似文献
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On the resolution and optimization of a system of fuzzy relational equations with sup-T composition 总被引:3,自引:2,他引:1
This paper provides a thorough investigation on the resolution of a finite system of fuzzy relational equations with sup-T composition, where T is a continuous triangular norm. When such a system is consistent, although we know that the solution set can be characterized
by a maximum solution and finitely many minimal solutions, it is still a challenging task to find all minimal solutions in
an efficient manner. Using the representation theorem of continuous triangular norms, we show that the systems of sup-T equations can be divided into two categories depending on the involved triangular norm. When the triangular norm is Archimedean,
the minimal solutions correspond one-to-one to the irredundant coverings of a set covering problem. When it is non-Archimedean, they only correspond to a subset of constrained irredundant coverings of a set covering problem. We then show that the problem of minimizing a linear objective function subject to a system of sup-T equations can be reduced into a 0–1 integer programming problem in polynomial time. This work generalizes most, if not all,
known results and provides a unified framework to deal with the problem of resolution and optimization of a system of sup-T equations. Further generalizations and related issues are also included for discussion. 相似文献
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This work considers solving the sup-T{\mathcal{T}} equation constrained optimization problems from the integer programming viewpoint. A set covering-based surrogate approach
is proposed to solve the sup-T{\mathcal{T}} equation constrained optimization problem with a separable and monotone objective function in each of the variables. This
is our first trial of developing integer programming-based techniques to solve sup-T{\mathcal{T}} equation constrained optimization problems. Our computational results confirm the efficiency of the proposed method and show
its potential for solving large scale sup-T{\mathcal{T}} equation constrained optimization problems. 相似文献
4.
The solution set of a consistent system of fuzzy relational equations with max-min composition can be characterized by one
maximum solution and a finite number of minimal solutions. A polynomial-time method of O(mn) complexity is proposed to determine whether such a system has a unique minimal solution and/or a unique solution, where
m, n are the dimensions of the input data. The proposed method can be extended to examining a system of fuzzy relational equations
with max-T composition where T is a continuous triangular norm. 相似文献
5.
In global optimization, a typical population-based stochastic search method works on a set of sample points from the feasible region. In this paper, we study a recently proposed method of this sort. The method utilizes an attraction-repulsion mechanism to move sample points toward optimality and is thus referred to as electromagnetism-like method (EM). The computational results showed that EM is robust in practice, so we further investigate the theoretical structure. After reviewing the original method, we present some necessary modifications for the convergence proof. We show that in the limit, the modified method converges to the vicinity of global optimum with probability one. 相似文献
6.
Hao Cheng Shu-Cherng Fang John E. Lavery 《Computational Optimization and Applications》2004,29(2):219-253
An active set based algorithm for calculating the coefficients of univariate cubic L
1 splines is developed. It decomposes the original problem in a geometric-programming setting into independent optimization problems of smaller sizes. This algorithm requires only simple algebraic operations to obtain an exact optimal solution in a finite number of iterations. In stability and computational efficiency, the algorithm outperforms a currently widely used discretization-based primal affine algorithm. 相似文献
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This paper studies the variational inequality problem over a fuzzy domain and variational inequalities for fuzzy mappings over a fuzzy domain. It is shown that such problems can be reduced to bilevel programming problems. A penalty function algorithm is introduced with a convergence proof. Numerical examples are also included to illustrate the solution procedure. 相似文献
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