求解非线性互补问题的内点正算法

基金项目: 湖南省自然科学基金资助项目(98JJY2053)

A Positve Interior-Point Algorithm for Nonlinear Complementarity Problems

1.
Guilin University of Electronic Technology, Guilin 545000, P. R. China;
2.
Institute of Mathematics, Academy of Mathematics & System Sciences, CAS, Beijing 100080, P. R. China;
3.
Department of Mathematic & Computer, Changsha University of Electric Power, Changsha 410077, P. R. China

摘要: 针对非线性互补问题,提出了与其等价的非光滑方程的内点正算法,并在一定条件下证明了该算法的收敛性定理。数值结果表明,该算法是十分有效的。
- 非线性互补问题 /
- 内点正算法 /
- 非光滑方程
Abstract: Anew iterative method, which is called positive interior-point algorithm, is presented for solving the nonlinear complementarity problems.This method is of the desirable feature of robustness.And the convergence theorems of the algorithm is established.In addition, some numerical results are reported.
- nonlinear complementarity problems /
- positive interior-point algorithm /
- non-smooth equations

[1]	Harker P T,Pang J S.Finite-dimensional variational inequality and nonlinear complemen tarity problems:a survey of theory,algorithms and applications[J].Math Prog,1990,48(2):161-220.
[2]	Harker P T,Xiao B.Newton's methods for nonlinear complementarity problem:a B-differentiable equation approach[J].Math Prog,1990,48(3):339-358.
[3]	Pang J S.Newton's method for B-differentiable equations[J].Math Oper Res,1990,15(2):311-341.
[4]	Monteriro R D C,Pang J S,Wang T.A Positive algorthm for nonlinear complementarity problem[J].SIAM J Opt,1995,5(1):129-148.
[5]	Pang J S.A B-differentiable equation-based,globally and locally quadratically convergent alogorithm for nonlinear problems[J].Math Prog,1991,51(1):101-131.
[6]	Pang J S.Gabriel S A.NE/SQP:a robust algorithm for nonlinear complementarity problems[J].Math Prog,1993,60(2):295-338.
[7]	Mathiesen L.An algorithm based on a sequence of linear complementarity problems applied to a Walrasian equilibrium model:an example[J].Math Prog,1987,37(1):1-18.
[8]	Friedlander A,Martinez J M,Stantos S A.A new strategy for solving variational inequalities in bounded polytopes[J].Numer Funct Anal and Optimiz,1995,16(5/6):653-668.