Let eRN be the usual vector-space of real N-uples with the usual inner product denoted by (., . ). In this paper P is a nonempty compact polyhedral set of mN, f is a real-valued function defined on (RN continuously differentiable and fP is the line- ly constrained minimization problem stated as: min (f(x) I x P) For computing stationary points of problemtj) we propose a method which attempts to operate within the linear-simplex method structure. This method then appears as a same type of method as the convex-simplex method of Zangwill 6]. It is however, different and has the advantage of...

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The International Institute for Applied Systems Analysis (IIASA) in Laxenburg, Austria, has been involved in research on nondifferentiable optimization since 1976. IIASA-based East-West cooperation in this field has been very productive, leading to many important theoretical, algorithmic and applied results. Nondifferentiable optimi zation has now become a recognized and rapidly developing branch of mathematical programming. To continue this tradition, and to review recent developments in this field, IIASA held a Workshop on Nondifferentiable Optimization in Sopron (Hungary) in September...

Pairs of compact convex sets arise in the quasidifferential calculus of V.F. Demyanov and A.M. Rubinov as sub- and superdifferentials of quasidifferen tiable functions (see 26]) and in the formulas for the numerical evaluation of the Aumann-Integral which were recently introduced in a series of papers by R. Baier and F. Lempio (see 4], 5], 10] and 9]) and R. Baier and E.M. Farkhi 6], 7], 8]. In the field of combinatorial convexity G. Ewald et al. 36] used an interesting construction called virtual polytope, which can also be represented as a pair of polytopes for the calculation of...