• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Central European journal of operations research: CEJOR >Nonlinear transformations for the simplification of unconstrained nonlinear optimization problems
【24h】

Nonlinear transformations for the simplification of unconstrained nonlinear optimization problems

机译：非线性变换，用于简化无约束非线性优化问题

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Formalization decisions in mathematical programming could significantly influence the complexity of the problem, and so the efficiency of the applied solver methods. This widely accepted statement induced investigations for the reformulation of optimization problems in the hope of getting easier to solve problem forms, e.g. in integer programming. These transformations usually go hand in hand with relaxation of some constraints and with the increase in the number of the variables. However, the quick evolution and the widespread use of computer algebra systems in the last few years motivated us to use symbolic computation techniques also in the field of global optimization. We are interested in potential simplifications generated by symbolic transformations in global optimization, and especially in automatic mechanisms producing equivalent expressions that possibly decrease the dimension of the problem. As it was pointed out by Csendes and Rapcsak (J Glob Optim 3(2):213-221, 1993), it is possible in some cases to simplify the unconstrained nonlinear objective function by nonlinear coordinate transformations. That means mostly symbolic replacement of redundant subexpressions expecting less computation, while the simplified task remains equivalent to the original in the sense that a conversion between the solutions of the two forms is possible. We present a proper implementation of the referred theoretical algorithm in a modern symbolic programming environment, and testing on some examples both from the original publications and from the set of standard global optimization test problems to illustrate the capabilities of the method.
机译：数学编程中的形式化决策可能会严重影响问题的复杂性，因此会影响所应用求解器方法的效率。这一被广泛接受的陈述引发了对优化问题的重新表述的研究，以期希望更容易地解决问题形式，例如在整数编程中。这些转换通常与一些约束的放宽和变量数量的增加齐头并进。然而，近几年来计算机代数系统的快速发展和广泛使用促使我们在全局优化领域也使用符号计算技术。我们对全局优化中的符号转换所产生的潜在简化感兴趣，尤其是对产生等效表达式的自动机制，这可能会减小问题的范围。正如Csendes和Rapcsak（J Glob Optim 3（2）：213-221，1993）所指出的那样，在某些情况下可以通过非线性坐标变换来简化无约束的非线性目标函数。这意味着冗余子表达式的符号替换主要是期望较少的计算，而简化的任务在某种意义上可以与两种形式的解决方案进行转换，因此与原始任务相当。我们介绍了在现代符号编程环境中引用的理论算法的正确实现，并通过原始出版物和标准全局优化测试问题集中的一些示例进行了测试，以说明该方法的功能。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号