Globally convergent successive approximation method for severely nonsmooth equations

Liqun Qi, Xiaojun Chen

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54 Citations (Scopus)


This paper presents a globally convergent successive approximation method for solving F(x) = 0 where F is a continuous function. At each step of the method, F is approximated by a smooth function fk, with ∥fk-F∥→0 as k→∞. The direction -fk′(xk)-1F(xk) is then used in a line search on a sum of squares objective. The approximate function fkcan be constructed for nonsmooth equations arising from variational inequalities, maximal monotone operator problems, nonlinear complementarity problems, and nonsmooth partial differential equations. Numerical examples are given to illustrate the method.
Original languageEnglish
Pages (from-to)402-418
Number of pages17
JournalSIAM Journal on Control and Optimization
Issue number2
Publication statusPublished - 1 Jan 1995
Externally publishedYes

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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