By virtue of the separation theorem of convex sets, a necessary condition and a sufficient condition for epsilon-vector equilibrium problem with constraints are obtained. Then, by using the Gerstewitz nonconvex separa...
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By virtue of the separation theorem of convex sets, a necessary condition and a sufficient condition for epsilon-vector equilibrium problem with constraints are obtained. Then, by using the Gerstewitz nonconvex separation functional, a necessary and sufficient condition for epsilon-vector equilibrium problem without constraints is obtained.
A branch and bound algorithm is proposed for globally solving a class of nonconvex programming problems (NP). For minimizing the problem, linear lower bounding functions (LLBFs) of objective function and constraint fu...
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A branch and bound algorithm is proposed for globally solving a class of nonconvex programming problems (NP). For minimizing the problem, linear lower bounding functions (LLBFs) of objective function and constraint functions are constructed, then a relaxation linear programming is obtained which is solved by the simplex method and which provides the lower bound of the optimal value. The proposed algorithm is convergent to the global minimum through the successive refinement of linear relaxation of the feasible region and the solutions of a series of linear programming problems. And finally the numerical experiment is reported to show the feasibility and effectiveness of the proposed algorithm. (C) 2008 Elsevier Ltd. All rights reserved.
In the papers [G.C. Feng, B. Yu, Combined homotopy interior point method for nonlinear programming problems, in: H. Fujita, M. Yamaguti (Eds.), Advances in Numerical Mathematics;Proceedings of the Second Japan-China S...
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In the papers [G.C. Feng, B. Yu, Combined homotopy interior point method for nonlinear programming problems, in: H. Fujita, M. Yamaguti (Eds.), Advances in Numerical Mathematics;Proceedings of the Second Japan-China Seminar on Numerical Mathematics, in: Lecture Notes in Numerical and Applied Analysis, vol. 14, Kinokuniya, Tokyo, 1995, pp. 9-16;G.C. Feng, Z.H. Lin, B. Yu, Existence of an interior pathway to a Karush-Kuhn-Tucker point of a nonconvex programming problem, Nonlinear Analysis 32 (1998) 761-768;Z.H. Lin, B. Yu, G.C. Feng, A combined homotopy interior point method for convex programming problem, Applied Mathematics and Computation 84(1997) 193-211], a combined homotopy interior method was presented and global convergence results obtained for nonconvex nonlinear programming when the feasible set is bounded and satisfies the so called normal cone condition. However, for when the feasible set is not bounded, no result has so far been obtained. In this paper, a combined homotopy interior method for nonconvex programming problems oil the unbounded feasible set is considered. Under suitable additional assumptions, boundedness of the homotopy path, and hence global convergence, is proven. (C) 2008 Elsevier Ltd. All rights reserved.
In this paper, a combined interior point homotopy method is used to solve constrained nonconvex programming problems. Some results for the homotopy pathway are obtained. It is known that a K-K-T point can be obtained ...
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In this paper, a combined interior point homotopy method is used to solve constrained nonconvex programming problems. Some results for the homotopy pathway are obtained. It is known that a K-K-T point can be obtained from this homotopy method, and it proves that, when the homotopy map is a regular map, the K-K-T point must be a local minimum point on choosing a proper homotopy equation. (C) 2009 Elsevier Ltd. All rights reserved.
This paper presents a novel optimization method for effectively solving nonconvex quadratically constrained quadratic programs (NQCQP) problem. By applying a novel parametric linearizing approach, the initial NQCQP pr...
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This paper presents a novel optimization method for effectively solving nonconvex quadratically constrained quadratic programs (NQCQP) problem. By applying a novel parametric linearizing approach, the initial NQCQP problem and its subproblems can be transformed into a sequence of parametric linear programs relaxation problems. To enhance the computational efficiency of the presented algorithm, a cutting down approach is combined in the branch and bound algorithm. By computing a series of parametric linear programs problems, the presented algorithm converges to the global optimum point of the NQCQP problem. At last, numerical experiments demonstrate the performance and computational superiority of the presented algorithm.
We study a nonlinear three-point boundary value problem of sequential fractional differential inclusions of order xi + 1 with n 1 = 2. Some new existence results for convex as well as nonconvex multivalued maps are ob...
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We study a nonlinear three-point boundary value problem of sequential fractional differential inclusions of order xi + 1 with n 1 < xi <= n, n >= 2. Some new existence results for convex as well as nonconvex multivalued maps are obtained by using standard fixed point theorems. The paper concludes with an example.
Under the condition that the values of the objective function and its subgradient are computed approximately, we introduce a cutting plane and level bundle method for minimizing nonsmooth nonconvex functions by combin...
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Under the condition that the values of the objective function and its subgradient are computed approximately, we introduce a cutting plane and level bundle method for minimizing nonsmooth nonconvex functions by combining cutting plane method with the ideas of proximity control and level constraint. The proposed algorithm is based on the construction of both a lower and an upper polyhedral approximation model to the objective function and calculates new iteration points by solving a subproblem in which the model is employed not only in the objective function but also in the constraints. Compared with other proximal bundle methods, the new variant updates the lower bound of the optimal value, providing an additional useful stopping test based on the optimality gap. Another merit is that our algorithm makes a distinction between affine pieces that exhibit a convex or a concave behavior relative to the current iterate. Convergence to some kind of stationarity point is proved under some looser conditions.
Some necessary global optimality conditions and sufficient global optimality conditions for nonconvex minimization problems with a quadratic inequality constraint and a linear equality constraint are derived. In parti...
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Some necessary global optimality conditions and sufficient global optimality conditions for nonconvex minimization problems with a quadratic inequality constraint and a linear equality constraint are derived. In particular, global optimality conditions for nonconvex minimization over a quadratic inequality constraint which extend some known global optimality conditions in the existing literature are presented. Some numerical examples are also given to illustrate that a global minimizer satisfies the necessary global optimality conditions but a local minimizer which is not global may fail to satisfy them.
This paper presents a global optimization algorithm for solving globally the generalized nonlinear multiplicative programming (MP) with a nonconvex constraint set. The algorithm uses a branch and bound scheme based on...
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This paper presents a global optimization algorithm for solving globally the generalized nonlinear multiplicative programming (MP) with a nonconvex constraint set. The algorithm uses a branch and bound scheme based on an equivalently reverse convex programming problem. As a result, in the computation procedure the main work is solving a series of linear programs that do not grow in size from iterations to iterations. Further several key strategies are proposed to enhance solution production, and some of them can be used to solve a general reverse convex programming problem. Numerical results show that the computational efficiency is improved obviously by using these strategies.
Urban traffic congestion has already become an urgent problem. Artificial societies, Computational experiments, and Parallel execution (ACP) method is applied to urban traffic problems. In ACP framework, optimization ...
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ISBN:
(纸本)9781479960798
Urban traffic congestion has already become an urgent problem. Artificial societies, Computational experiments, and Parallel execution (ACP) method is applied to urban traffic problems. In ACP framework, optimization for urban road networks achieves remarkable effect. Optimization for urban road networks is a problem of nonlinear and non-convex programming with typical large-scale continual and integer variables. Due to the complicated urban traffic system, this paper focuses on the ACP-based Computational experiments modeling. It hopes to find an optimization model that is further accord with the practical situation. To this end, we use a mixed integer nonlinear programming problem (MINLP) and an genetic algorithm (GA) for urban road networks optimization. The systemic simulation experiments show that the approach is more effective in improving traffic status and increasing traffic safety.
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