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Mathematical Programming with Data Perturbations
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Presents research contributions and tutorial expositions on current methodologies for sensitivity, stability and approximation analyses of mathematical programming and related problem structures involving parameters. The text features up-to-date findings on important topics, covering such areas as the effect of perturbations on the performance of algorithms, approximation techniques for optimal control problems, and global error bounds for convex inequalities.
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Discretization and mesh-independent of Newton's method for generalized differentiability of optimal solutions in non-linear parametric optimization; characterisations of Lipschitzian stability in nonlinear programming; on second order sufficient conditions for structured nonlinear programs in infinite-dimensional function spaces; algorithmic stability analysis for certain trust region methods; a note on using linear knowledge to solve efficiency linear programs specified with approximate data; on the role of the Mangasarian-Fromovitz constraint qualification for penalty-, exact penalty-, and Lagrange multiplier methods; Hoffman's error bound for systems of convex functions and applications to nonlinear optimization; on well-posedness and stability analysis optimization; convergence of approximations to nonlinear optimal control problems; a perturbation-based duality classification for max-flow min-cut problems of Strang and Iri; central and peripheral results in the study of marginal and performance functions; topological stability of feasible sets in semi-infinite optimization - a tutorial; solution existence for infinite quadratic programming; sensitivity analysis of nonlinear programming problems via minimax functions; parametric linear complementary problems; sufficient conditions for weak sharp minima of order two and directional derivatives of the value function.

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