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论文类型：期刊论文

发表时间：2014-07-01

发表刊物：JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION

收录刊物：Scopus、SSCI、SCIE

卷号：10

期号：3

页面范围：717-741

ISSN号：1547-5816

关键字：Principal-agent model; piecewise linear contractual function; homotopy method; bilevel programming; nonconvex programming

摘要：In this paper, to design a piecewise linear contractual function, we consider to solve the single-level nonconvex programming with integral operator which is equivalent to the principal-agent bilevel programming model with continuous distribution. A modified constraint shifting homotopy method for solving the Karush-Kuhn-Tucker system of the discrete nonconvex programming is proposed and the global convergence from any initial point in shifted feasible set is proven under some mild conditions. A simple homotopy path tracing algorithm is given and is implemented in Mat lab. For some typical risk averse utility functions and the typical distribution functions which simultaneously satisfy monotone likelihood ratio condition and convexity of the distribution function condition, some numerical tests to design the piecewise linear contract are done by our homotopy method as well as by using fmincon in Mat lab, LOQO and MINOS and, as a comparison, the piecewise constant contracts are also designed by solving the single-level nonconvex programming which is equivalent to the principal-agent bilevel programming model with corresponding discrete distributions. Numerical tests show that: to design a piecewise linear contract, which is much better than a piecewise constant contract, it needs only to solve a much lower dimensional optimization problem and hence needs much less computing time. Numerical experiences also show that the modified constraint shifting homotopy method is feasible and robust.