Globally optimal univariate spline approximations
研究了单变量最小二乘样条逼近的全局最优解问题，提出混合整数二次约束规划和分支定界两种方法，在真实和合成数据集上验证了可行性。
Abstract We revisit the problem of computing optimal spline approximations for univariate least-squares splines from a combinatorial optimization perspective. In contrast to most approaches from the literature we aim at globally optimal coefficients as well as a globally optimal placement of a fixed number of knots for a discrete variant of this problem. To achieve this, two different possibilities are developed. The first approach that we present is the formulation of the problem as a mixed-integer quadratically constrained problem, which can be solved using commercial optimization solvers. The second method that we propose is a branch-and-bound algorithm tailored specifically to the combinatorial formulation. We compare our algorithmic approaches empirically on both, real and synthetic curve fitting data sets from the literature. The numerical experiments show that our approach to tackle the least-squares spline approximation problem with free knots is able to compute solutions to problems of realistic sizes within reasonable computing times.