Convex Optimization & Euclidean Distance Geometry
Convex Optimization & Euclidean Distance Geometry
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发表时间：
2004
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通讯作者：
J. Dattorro
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作者：
J. Dattorro
优化是在面对相互冲突的需求时做出最佳选择的科学。任何凸优化问题都有几何解释。如果给定的优化问题可以转化为凸等价问题，那么就获得了这种解释性的好处。这是一个强大的吸引力：能够将优化问题的几何图形可视化。相反，几何学的最新进展将凸优化置于其证明的核心。这本书是关于凸优化，凸几何（特别注意距离几何），几何问题，和问题，可以转化为几何问题。欧几里得距离几何基本上是从点间距离信息确定点的构象；例如，仅给定距离信息，确定是否存在对应的点的可实现配置；在某个维度上达到给定点间距离的点的列表。大型黑白平装
Optimization is the science of making a best choice in the face of conflicting requirements. Any convex optimization problem has geometric interpretation. If a given optimization problem can be transformed to a convex equivalent, then this interpretive benefit is acquired. That is a powerful attraction: the ability to visualize geometry of an optimization problem. Conversely, recent advances in geometry hold convex optimization within their proofs' core. This book is about convex optimization, convex geometry (with particular attention to distance geometry), geometrical problems, and problems that can be transformed into geometrical problems. Euclidean distance geometry is, fundamentally, a determination of point conformation from interpoint distance information; e.g., given only distance information, determine whether there corresponds a realizable configuration of points; a list of points in some dimension that attains the given interpoint distances. large black & white paperback