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Titlebook: Mathematical Programming at Oberwolfach; H. König,B. Korte,K. Ritter Book 1981Latest edition Springer-Verlag Berlin Heidelberg 1981 Mathem

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Algorithmic versus axiomatic definitions of matroids,nd calculations of the complexity of matroid properties with respect to various “oracles”. Of particular interest is the fact that matroids can be also axiomatically defined by a girth function and that the GIRTH oracle is significantly stronger than the more standard oracles.
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,On conditions warranting Φ-subdifferentiability,e a neighbourhood . of .., a neighbourhood . of .. and a constant .>0 such that for .∃..The investigations of γ-paraconvexity were stimulated by investigations of Hölder and Lipschitz differentiability of Lagrangians considered by Dolecki and Kurcyusz in [8].
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Linear programming by an effective method using triangular matrices, constraint becomes inactive, the computational effort in solving the triangular systems corresponds to that of the matrix-updating in the projection method, whereas in all other cases the effort is reduced. This reduction can be very high. Cycling of the method is excluded by a very simple rule.
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Secant approximation methods for convex optimization,bounds on the optimal value are derived from the piecewise-linear approximations. Convergence to the optimal value of the given problem is established under mild hypotheses. The method has been successfully tested on a variety of problems, including a water supply problem with more than 900 variables and 600 constraints.
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