非完整Optimization中的Lagrange对偶和Wolf对偶
Lagrange and Wolf Dualities in Nonholonomic Optimization
摘要：
本文讨论微分几何和力学中的最优化问题，按其所需的约束类型分为完整约束和非完整约束。中心问题与对偶非完整程序有关（它们意味着什么以及如何求解？）当不完整约束由Pfaff方程给出时，最初的结果是令人惊讶的，包括来自Vranceanu理论的非完整流形，从几何分布理论和达布定理的典范坐标，我们可以表示普法夫形式。在这些方法中，我们还得到一个原始的黎曼几何附加到一个给定的约束最优化问题。
英文摘要：
This article deals with optimizing problems classified by the kinds of restrictions as required in differential geometry and in mechanics: holonomic and nonholonomic. The central issue relates to dual nonholonomic programs (what they mean and how they are solved?) when the nonholonomic constraints are given by Pfaff equations. The original results are surprising and include aspects derived from the Vranceanu theory of nonholonomic manifolds, from the geometric distributions theory and from Darboux's theorem on canonical coordinates in which we can express a Pfaff form. On these ways we get also an original Riemannian geometry attached to a given constrained optimization problem.
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