Continuation Methods for Nonlinear ProgrammingUniversity of Wisconsin--Madison, 1989 - 322 pages |
Contents
Theoretical background and literature review | 2 |
Generalized equations | 16 |
Newtons method for nonsmooth equations and constrained | 36 |
Common terms and phrases
A(xº ALGORITHM 5.1 Assume B-differentiable equations Chapter classical continuation process computational experience constrained optimization continuous solution path continuous with modulus convex set defined developed directional derivative directionally differentiable exists F-differentiable Hence homeomorphism homotopy method iteration map Lemma Let f line search linear linear complementarity problems linear independence Lipschitz continuous Mangasarian Mathematical Programming method for nonlinear Minimize modified continuation process multiple-path continuation method Nc(y neighborhood Newton method nonlinear equations equivalent nonlinear programming nonsingular nonsmooth equations nonsmooth functions open subset Ortega & Rheinboldt parameter point-based approximation Proof Proposition 3.2 quadratic programming quadratic programming problem Rheinboldt 70 Robinson 88b S.M. Robinson satisfies the optimality Section sensitivity analysis based single-path continuation method smooth SNLP solves stability and sensitivity starting point Subject to p(x Theorem 4.1 Theorem Let tion unique solution x⁰ y⁰