具有性能约束几何布局优化模型的研究

On optimal models of geometric layout with behavioural constraints

建立了带性能约束圆域内几何布局优化问题的各种数学模型，其中图元 可为圆形、三角形及任意连通的二维几何图形。通过引入模函数与广义距离 函数等概念，详细论述了此类几何布局问题可转化为含有Ｄ．Ｃ．约束的凸规 划问题，从而为进一步研究几何布局优化问题的最优性条件、优化算法等奠 定了数学基础。

This paper aims at establishing mathematical models for the problems of geometric layout with behavioural constraints over various 2-dimensional connected regions. It is shown that this kind of layout problem may be reduced, via the introduced concepts such as norm function and generalized distance function, to a convex programming with D. C. constraints. This approach provides a mathematical reasoning to the discussion of the geometrit layout problem, optimal conditions and optimization methods.