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Название: MATHEMATICAL PROGRAMMING STUDY 19. Optimality and stability in mathematical programming
Автор: Guignard M.
The last decade has seen a number of improvements regarding the theory of optimality in mathematical programming, in particular concerning characterization of optimality for broad classes of problems. Increasingly sophisticated types of optimality conditions are studied and more general types of problems can now be considered: nonsmooth, nonconvex, nondifferentiable, etc. New tools have been developed which permit these advances, such as generalized gradients, subgradients, generalized equations, cones of directions of constancy, faithful convexity, normal subcones, semiconvexity, semidifferentiability, just to name a few. Characterizations of optimality have been proposed with or without constraint qualifications. At the same time, linear complementarity theory grew out of infancy both from a computational and a theoretical viewpoint. For either type of problem, characterizations of the existence of bounded solutions and/or bounded sets of multipliers and the effect of small perturbations of the data on the solutions, the multipliers and/or the optimum have been thoroughly studied, and considerable progress has been made.
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