NEWTON AND QUASI-NEWTON METHODS FOR EQUATIONS OF SMOOTH COMPOSITIONS OF SEMISMOOTH FUNCTIONS

  • Gao, Yan (Department of Mathematics and Physics Yanshan University)
  • 발행 : 1999.09.01

초록

The Newtom method and the quasi-Newton method for solving equations of smooth compositions of semismooth functions are proposed. The Q-superlinear convergence of the Newton method and the Q-linear convergence of the quasi-Newton method are proved. The present methods can be more easily implemeted than previous ones for this class of nonsmooth equations.

키워드

참고문헌

  1. Science in China(Ser.A.) v.39 no.5 Variational principle with nonlinear complementarity for three dimensional contact problems and its numerical method W.Chen;G.Chen;E.Feng
  2. Computing v.58 A verification method for solutions of nonsmooth equations X.Chen
  3. Optimization and Nonsmooth Analysis F.H.Ckarke
  4. Engineering and Economic Quasidifferentiability and Nonsmooth Modeling in Mechanics V.F.Demyanov;G.E.Stavroulakis;L.N.Polyakova;P.D.Panagiotopoulous
  5. Archives of Control Sciences v.3(XXXIX) no.3;4 Finding a Clarke subgradient for smooth composition of max-type functions Y.Gao;Z.Q.Xia
  6. J. Dalian University of Technology v.38 no.6 Second-order directional derivatives for max-type functions F.W.Meng;Y.Gao;Z.Q.Xia
  7. SIAM J. Control and Optimization v.15 Semismooth and semiconvex functions in constrained optimization M.Mifflin
  8. Iterative Solution of Nonlinear Equations in Serveral Variables J.M.Ortega;W.C.Rheinboldt
  9. Mathematics of Operations Research v.18 no.1 Convergence analysis of some algorithms for solving nonsmooth equations L.Qi
  10. Mathematical Programming v.58 A nonsmooth version of Newton's method L.Qi;J.Sun
  11. SIAM J. Optimization v.7 no.2 Newton and quasi-Newton methods for a class of nonsmooth equations and related problems D.Sun;J.Han