By Pang J.

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**Extra info for A B-differentiable equation-based, globally and locally quadratically convergent algorithm for nonlinear programs, complementarity and variational inequality problems**

**Example text**

T. S. L. Allgower and K. , Computational Solution of Nonlinear ,Systems of Equations. Lectures in Applied Mathematics No. 26 (American Mathematical Society, Providence, RI, 1990) pp. 265-284. T. Harker and B. Xiao, "Newton's method for the nonlinear complementarity problem: a B-ditterentiable equation approach," Mathematical Programming (Series B) 48 (1990) 339-358. H. Josephy, "Newton's method for generalized equation," Technical summary report 1965, Mathematics Research Center, University of Wisconsin-Madison (Madison, WI, 1979).

Conclusion In this paper, we have presented a unified descent algorithm for solving a general nonlinear program, the nonlinear complementarity problem and the variational inequality problem. We have established the global and locally quadratic convergence of the algorithm and showed that the Maratos phenomenon cannot occur in Jong-Shi Pang / A B-differentiable equation based method 131 the algorithm. The algorithm is based on a common formulation of these classes of mathematical programs as a certain nonsmooth system of equations.

We have established the global and locally quadratic convergence of the algorithm and showed that the Maratos phenomenon cannot occur in Jong-Shi Pang / A B-differentiable equation based method 131 the algorithm. The algorithm is based on a common formulation of these classes of mathematical programs as a certain nonsmooth system of equations. Several future research possibilities exist. The extension of the algorithm to allow for approximation matrices to replace the exact Jacobian VxL(z k) is important for large-scale problems; the idea of inexact solution of the subproblems and the corresponding convergence theory, as well as the treatment of subproblems with no solution all deserve a closer investigation; the numerical performance of the algorithm needs to be understood; and finally, the generalization of the ideas contained herein to other non-ditterentiable optimization and/or equation-solving problems is worthy of study.