Zbl 1108.90001
Ruszczynski,
Andrzej
Nonlinear optimization. (English)
[B] Princeton, NJ: Princeton University Press. xii, 448~p. \sterling~38.95;
\$~59.50 (2006). ISBN 0-691-11915-5/hbk
This is one of the best textbooks on nonlinear optimization I know. Focus is on
both theory and algorithmic solution of convex as well as of differentiable
programming problems. Very helpful are many examples, exercises and interesting
applications. The interested reader can find carefully formulated proofs of the
results. Initial point is convex analysis including sub\-differential calculus
and conjugate duality. Very interesting is the approach to the formulation of
(necessary and sufficient) optimality conditions which uses metric regularity
and normal cones to the feasible set. The conditions are formulated both for nondifferentiable (convex) and for differentiable
optimization problems. Besides Lagrangean duality
also the augmented Lagrangean is investigated. In the
part on algorithms besides algorithms for differentiable programming problems
also algorithms for nondifferentiable convex problems
are explained. Focus is on proximal point, bundle and trust region algorithms.
Besides unconstraint problems also an exact penalty approach for the
minimization subject to nonlinear constraints is considered. In this part, not
only convergence proofs but also results on convergence speed are included.
[Stephan
Dempe (Freiberg)]
MSC 2000:
*90-01
Textbooks (optimization)
90C25
Convex programming
90C30
Nonlinear programming
Keywords: optimality
conditions; solution algorithms; duality; convex programming; nondifferentiable programming
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