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论文类型：期刊论文

发表时间：2018-03-01

发表刊物：COMPUTATIONAL & APPLIED MATHEMATICS

收录刊物：SCIE

卷号：37

期号：1

页面范围：541-566

ISSN号：0101-8205

关键字：Principal-agent model; Piecewise linear contractual function; Homotopy method; Nonconvex programming; Simpson's rule

摘要：In this paper, the principal-agent bilevel programming problem with integral operator is considered, in which the upper-level object is the agent that maximizes its expected utility with respect to an agreed compensation contract. The constraints are the principal's participation and the agent's incentive compatibility. The latter is a lower-level optimization problem with respect to its private action. To solve an equivalent single-level nonconvex programming problem with integral operator, a modified homotopy method for solving the Karush-Kuhn-Tucker system is proposed. This method requires only an interior point and, not necessarily, a feasible initial approximation for the constraint shifting set. Global convergence is proven under some mild conditions. Numerical experiments were performed by our homotopy method as well as by fmincon in Matlab, LOQO and MINOS. The experiments showed that: designing a piecewise linear contract is much better than designing a piecewise constant contract and only needs to solve a much lower-dimensional optimization problem and hence needs much less computation time; the optimal value of the principal-agent model with designing piecewise linear contract tends to a limitation, while the discrete segments gradually increase; and finally, the proposed modified homotopy method is feasible and effective.