共查询到18条相似文献,搜索用时 156 毫秒
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本文提出了一种求Hilbert空间中给定点x0在两个多面体K’与K”之交上的最佳逼近的算法,它把问题化归为有限次求点在K’与K”中的最佳逼近的问题.由于保凸回归问题可表述为求某点x0在两个锐锥之交上的最佳逼近问题,故结合熟知的锐锥逼近的PAVA算法即可得到保凸回归的有限算法.文章还计算了一个保凸回归问题的实例. 相似文献
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论可微函数的共单调逼近和共凸逼近 总被引:2,自引:0,他引:2
对有限区间上可微函数借助于代数多项式的共单调逼近和共凸逼近的逼近度估计建立了更为精确的Jackson型不等式,扩充和改进了近期的一些结果。 相似文献
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本文对不等式约束优化问题给出了低阶精确罚函数的一种光滑化逼近.提出了通过搜索光滑化后的罚问题的全局解而得到原优化问题的近似全局解的算法.给出了几个数值例子以说明所提出的光滑化方法的有效性. 相似文献
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凸约束优化问题的带记忆模型信赖域算法 总被引:1,自引:0,他引:1
本文我们考虑求解凸约束优化问题的信赖域方法 .与传统的方法不同 ,我们信赖域子问题的逼近模型中包括过去迭代点的信息 ,该模型使我们可以从更全局的角度来求得信赖域试探步 ,从而避免了传统信赖域方法中试探步的求取完全依赖于当前点的信息而过于局部化的困难 .全局收敛性的获得是依靠非单调技术来保证的 相似文献
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A convexification method for a class of global optimization problems with applications to reliability optimization 总被引:1,自引:0,他引:1
A convexification method is proposed for solving a class of global optimization problems with certain monotone properties. It is shown that this class of problems can be transformed into equivalent concave minimization problems using the proposed convexification schemes. An outer approximation method can then be used to find the global solution of the transformed problem. Applications to mixed-integer nonlinear programming problems arising in reliability optimization of complex systems are discussed and satisfactory numerical results are presented. 相似文献
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We consider a convexification method for a class of nonsmooth monotone functions. Specifically, we prove that a semismooth
monotone function can be converted into a convex function via certain convexification transformations. The results derived
in this paper lay a theoretical base to extend the reach of convexification methods in monotone optimization to nonsmooth
situations.
Communicated by X. Q. Yang
This research was partially supported by the National Natural Science Foundation of China under Grants 70671064 and 60473097
and by the Research Grants Council of Hong Kong under Grant CUHK 4214/01E. 相似文献
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Monotone optimization problems are an important class of global optimization problems with various applications. In this paper,
we propose a new exact method for monotone optimization problems. The method is of branch-and-bound framework that combines
three basic strategies: partition, convexification and local search. The partition scheme is used to construct a union of
subboxes that covers the boundary of the feasible region. The convexification outer approximation is then applied to each
subbox to obtain an upper bound of the objective function on the subbox. The performance of the method can be further improved
by incorporating the method with local search procedure. Illustrative examples describe how the method works. Computational
results for small randomly generated problems are reported.
Dedicated to Professor Alex Rubinov on the occasion of his 65th birthday. The authors appreciate very much the discussions
with Professor Alex Rubinov and his suggestion of using local search. Research supported by the National Natural Science Foundation
of China under Grants 10571116 and 10261001, and Guangxi University Scientific Research Foundation (No. X051022). 相似文献
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A general monotonization method is proposed for converting a constrained programming problem with non-monotone objective function and monotone constraint functions into a monotone programming problem. An equivalent monotone programming problem with only inequality constraints is obtained via this monotonization method. Then the existing convexification and concavefication methods can be used to convert the monotone programming problem into an equivalent better-structured optimization problem. 相似文献
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A kind of general convexification and concavification methods is proposed for solving some classes of global optimization problems with certain monotone properties. It is shown that these minimization problems can be transformed into equivalent concave minimization problem or reverse convex programming problem or canonical D.C. programming problem by using the proposed convexification and concavification schemes. The existing algorithms then can be used to find the global solutions of the transformed problems. 相似文献
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We show in this paper that via certain convexification, concavification and monotonization schemes a nonconvex optimization problem over a simplex can be always converted into an equivalent better-structured nonconvex optimization problem, e.g., a concave optimization problem or a D.C. programming problem, thus facilitating the search of a global optimum by using the existing methods in concave minimization and D.C. programming. We first prove that a monotone optimization problem (with a monotone objective function and monotone constraints) can be transformed into a concave minimization problem over a convex set or a D.C. programming problem via pth power transformation. We then prove that a class of nonconvex minimization problems can be always reduced to a monotone optimization problem, thus a concave minimization problem or a D.C. programming problem. 相似文献
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In this paper a successive optimization method for solving inequality constrained optimization problems is introduced via a parametric monotone composition reformulation. The global optimal value of the original constrained optimization problem is shown to be the least root of the optimal value function of an auxiliary parametric optimization problem, thus can be found via a bisection method. The parametric optimization subproblem is formulated in such a way that it is a one-parameter problem and its value function is a monotone composition function with respect to the original objective function and the constraints. Various forms can be taken in the parametric optimization problem in accordance with a special structure of the original optimization problem, and in some cases, the parametric optimization problems are convex composite ones. Finally, the parametric monotone composite reformulation is applied to study local optimality. 相似文献
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《Optimization》2012,61(6):605-625
A class of convexification and concavification methods are proposed for solving some classes of non-monotone optimization problems. It is shown that some classes of non-monotone optimization problems can be converted into better structured optimization problems, such as, concave minimization problems, reverse convex programming problems, and canonical D.C. programming problems by the proposed convexification and concavification methods. The equivalence between the original problem and the converted better structured optimization problem is established. 相似文献