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首页> 外文期刊>Mathematical methods of operations research >Generation of interior points and polyhedral representations of cones in cut by planes sharing a common point
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Generation of interior points and polyhedral representations of cones in cut by planes sharing a common point

机译：由共享公共点的平面切割的圆锥的内部点和多面体表示的生成

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摘要

The following paper describes a method for solving certain non-convex minimization problems. These problems contain properties where the feasible region may be represented as a union of convex cones. This set of cones is generated by the intersection of finitely many half-spaces passing through a defined origin. Globally the problem is non-convex, but it is locally convex within the interior of the generated cones whereas the objective function tends to infinity elsewhere. The following algorithm results in a polyhedral representation of all of the cones and an interior point in each of them. In order to solve the problem globally, a convex optimization algorithm is required to be initialized at each interior point and to converge to the local minimum over the corresponding cone. The best of these solutions is the global optimum. A study of the time complexity is presented herewith along with a detailed computational analysis.
机译：下文描述了一种解决某些非凸最小化问题的方法。这些问题包含一些属性，其中可行区域可以表示为凸锥的并集。这组圆锥体由穿过定义的原点的有限多个半空间的交集生成。从整体上讲，该问题是非凸的，但在生成的圆锥体内部是局部凸的，而目标函数在其他地方趋于无穷大。下列算法可得出所有圆锥体的多面体表示，以及每个圆锥体内的内点。为了整体解决该问题，需要在每个内部点初始化凸优化算法，并将其收敛到相应圆锥体上的局部最小值。这些解决方案中最好的就是全局最优。随即提出了对时间复杂度的研究以及详细的计算分析。

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