标题： 斜率临界问题 显示英文标题

标题： Skew critical problems

摘要： 非对称临界问题出现在连续和离散的非完整拉格朗日系统中。它们是约束优化问题的类比，其中目标函数在给定的先验分布方向上进行微分，而不是在约束的切向方向上进行微分。我们证明了非退化非对称临界问题的半全局存在性和唯一性，并表明两个非对称临界问题的解与这些问题本身具有相同的接触。此外，我们开发了一些必要的基础设施，以便在流形上直接几何地计算接触阶数。 显示英文摘要

摘要： Skew critical problems occur in continuous and discrete nonholonomic Lagrangian systems. They are analogues of constrained optimization problems, where the objective is differentiated in directions given by an apriori distribution, instead of tangent directions to the constraint. We show semiglobal existence and uniqueness for nondegenerate skew critical problems, and show that the solutions of two skew critical problems have the same contact as the problems themselves. Also, we develop some infrastructure that is necessary to compute with contact order geometrically, directly on manifolds.