Globally convergent method for designing twice spline contractual function

Zhichuan Zhu,Mihai Postolache,Yonghong Yao

doi:10.1186/s13660-019-2243-z

Abstract

To design a quadratic spline contractual function in the case of discretely unknown nodes, a modified constraint shifting homotopy algorithm for solving principal–agent problems is constructed in the paper. Then the existence of globally convergent solution to KKT systems for the principal–agent problem with spline contractual function is proved under a much weaker condition. The proposed algorithm only requires that any initial point is in the shifted feasible set but not necessarily in the original feasible set.

Highlights

Since the principal–agent model was proposed, an efficient and conventional method for analyzing the problem (1) was the so-called first-order approach
Since the problem (1) is an infinite-dimensional nonconvex bilevel programming, lots of papers have focused on the theoretical analysis of the validity on firstorder approach, few papers were presented for directly solving the principal–agent model
Cecchini et al [18] solved numerically the principal–agent problems written as a linear-exponential-normal model by solving bilevel programming problems using the ellipsoid algorithm in the case of assuming the performance measures is linear

Summary

Introduction

Since the principal–agent model was proposed, an efficient and conventional method for analyzing the problem (1) was the so-called first-order approach. Zhu and Yu [22] proposed another modified homotopy method for computing the solution to its KKT systems under requiring only an interior point and, not necessarily, a feasible initial approximation for the constraint shifting set.

Results

Conclusion