This book presents comprehensive state-of-the-art theoretical
analysis of the fundamental Newtonian and Newtonian-related
approaches to solving optimization and variational problems. A
central focus is the relationship between the basic Newton scheme
for a given problem and algorithms that also enjoy fast local
convergence. The authors develop general perturbed Newtonian
frameworks that preserve fast convergence and consider specific
algorithms as particular cases within those frameworks, i.e., as
perturbations of the associated basic Newton iterations. This
approach yields a set of tools for the unified treatment of various
algorithms, including some not of the Newton type per se. Among the
new subjects addressed is the class of degenerate problems. In
particular, the phenomenon of attraction of Newton iterates to
critical Lagrange multipliers and its consequences as well as
stabilized Newton methods for variational problems and stabilized
sequential quadratic programming for optimization. This volume will
be useful to researchers and graduate students in the fields of
optimization and variational analysis.
General
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