Globally and Superlinearly Convergent Algorithms for Nonlinear Programming |
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accumulation point active constraints bounded Chapter Computer convergence properties convergent exact penalty convex function defined exact penalty algorithms exact penalty function exists feasible point Garcia and Mangasarian globally and superlinearly globally convergent exact go to step Hence the proof Hessian i+1 i+1 iɛL implies infeasible Jacobian nonsingularity conditions jɛI Kuhn-Tucker conditions Kuhn-Tucker point lemma linear linear program linearly independent Lipchitz continuous LS(x¹ nonlinear program nxn matrix P(v¹ point of P(0,x point of problem possesses the convergence quadratic program quasi-Newton iterates Quasi-Newton Method sequence x¹ si+l stationary point stepsize procedure sufficiently close superlinearly convergent algorithms thesis ui+1 ui+l unconstrained University of Wisconsin updating schemes Vɛg vf(x vVf(x wi+l x²-x xi+l