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作者：Khachiyan, LG
摘要：Let A be a set of m points in R(n). We show that the problem of (1 + epsilon)n-rounding of A,, i.e., the problem of computing an ellipsoid E subset of or equal to R(n) such that [(1 + epsilon)n](-1)E subset of or equal to conv. hull(A) subset of or equal to E, can be solved in O(mn(2)(epsilon(-1) + In n + In In m)) arithmetic operations and comparisons. This result implies that the problem of approximating the minimum volume ellipsoid circumscribed about A can be solved in O(m(3.5) In(m epsilo...
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作者：Pang, JS; Ralph, D
作者单位：University of Melbourne
摘要：This paper is concerned with properties of the Euclidean projection map onto a convex set defined by finitely many smooth, convex inequalities and affine equalities. Under a constant rank constraint qualification, we show that the projection map is piecewise smooth (PC1) hence B(ouligand)-differentiable, or directionally differentiable; and a relatively simple formula is given for the B-derivative. These properties of the projection map are used to obtain inverse and implicit function theorems...
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作者：Bertsimas, D; Nino-Mora, J
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We show that if performance measures in stochastic and dynamic scheduling problems satisfy generalized conservation laws, then the feasible region of achievable performance is a polyhedron called an extended polymatroid, that generalizes the classical polymatroids introduced by Edmonds. Optimization of a linear objective over an extended polymatroid is solved by an adaptive greedy algorithm, which leads to an optimal solution having an indexability property (indexable systems). Under a certain...
