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

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I0. 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.

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). [8] N. D. thesis, University of London (London, 1978). P. McCormick, Nonlinear Programming: Theory, Algorithms, and Applications (Wiley, New York, 1983).

S. Pang and D. Chan, "Iterative methods for variational and complementarity problems," Mathematical programming 24 (1982) 284-313. M. Robinson, "Strongly regular generalized equations," Mathematics of Operations Research 5 (1980) 43-62.

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