论文标题
分段多项式插值函数方法，用于解决非线性编程问题与可行区域的非线性编程问题：数学证明
Piecewise Polynomial Interpolation Function Approach for Solving Nonlinear Programming Problems with Disjoint Feasible Regions: Mathematical Proofs
论文作者
论文摘要
分段多项式插值（PPI）函数方法旨在解决与可行区域不同的非线性编程问题。在此类问题中，脱节通常与禁止的操作区域有关，这与不允许变量假设的值频段相对应。这种禁止的操作区域的分析含义是使目标函数及其域不连续。 PPI函数方法包括通过等效的平等和不平等约束来代替与禁止操作区域相关的约束，从而允许应用任何基于基于梯度的优化方法来解决等效问题。在本文中，我们介绍了PPI函数的定义，并为其属性提供了数学证明。
The Piecewise Polynomial Interpolation (PPI) function approach is aimed at solving nonlinear programming problems with disjoint feasible regions. In such problems, disjointedness is generally associated with prohibited operating zones, which correspond to bands of values that a variable is not allowed to assume. An analytical implication of such prohibited operating zones is to make the objective function, as well as its domain, discontinuous. The PPI function approach consists in replacing the constraints associated with prohibited operating zones by an equivalent set of equality and inequality constraints, thereby allowing the application of any efficient gradient-based optimization method for solving the equivalent problem. In this paper, we present the definition of the PPI function and provide the mathematical proofs for its properties.
