The problem of monotone smoothing splines with bounds is formulated as a constrained minimization problem of the calculus of variations. Existence and uniqueness of solutions of this problem is proved, as well as the equivalence of it to a finite dimensional but nonlinear optimization problem. A new algorithm for computing the solution which is a spline curve, using a branch and bound technique, is presented. The method is applied to examples in neuroscience and for fitting cumulative distribution functions from data.

中文翻译：

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带边界的单调平滑样条

带边界的单调平滑样条曲线的问题被公式化为变化演算的约束最小化问题。证明了该问题解的存在唯一性，以及它与有限维但非线性优化问题的等价性。提出了一种使用分支定界技术计算样条曲线的新算法。该方法适用于神经科学领域的实例，并用于根据数据拟合累积分布函数。