Direct solutions to tropical optimization problems with nonlinear objective functions and boundary constraints
Direct solutions to tropical optimization problems with nonlinear objective functions and boundary constraints
复制标题
DOI：
--
复制
发表时间：
2013-11
期刊：
影响因子：
--
通讯作者：
N. Krivulin;K. Zimmermann
中科院分区：
文献类型：
--
作者：
N. Krivulin;K. Zimmermann
我们研究两个多维优化问题，制定热带数学。这些问题是最小化非线性目标函数，这些目标函数是通过幂等半域上有限维半模的向量上的乘法共轭向量转置来定义的，并且受到边界约束。的解决方案的方法，它涉及到推导的目标函数上的尖锐的界限，其次是确定的向量，产生的界限。基于该方法，直接的解决方案的问题得到了一个紧凑的向量形式。为了说明，我们将结果应用于求解约束Chebyshev逼近和定位问题，并给出数值例子。
We examine two multidimensional optimization problems that are formulated in terms of tropical mathematics. The problems are to minimize nonlinear objective functions, which are defined through the multiplicative conjugate vector transposition on vectors of a finite-dimensional semimodule over an idempotent semifield, and subject to boundary constraints. The solution approach is implemented, which involves the derivation of the sharp bounds on the objective functions, followed by determination of vectors that yield the bound. Based on the approach, direct solutions to the problems are obtained in a compact vector form. To illustrate, we apply the results to solving constrained Chebyshev approximation and location problems, and give numerical examples.