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作者：TAMIR, A
摘要：We prove that a bounded generalized polymatroid has a least weakly submajorized (supermajorized) vector. Such a vector simultaneously minimizes every nondecreasing (nonincreasing), symmetric and quasi-convex function defined on the generalized polymatroid. The same result herds also for the set of integer vectors of a bounded integral generalized polymatroid. We then extend these results to more general sets, and discuss several computational aspects.
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作者：IUSEM, AN; TEBOULLE, M
作者单位：Tel Aviv University
摘要：The phi-divergence proximal method is an extension of the proximal minimization algorithm, where the usual quadratic proximal term is substituted by a class of convex statistical distances, called phi-divergences. In this paper, we study the convergence rate of this nonquadratic proximal method for convex and particularly linear programming. We identify a class of phi-divergences for which superlinear convergence is attained both for optimization problems with strongly convex objectives at the...
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作者：SAIGAL, R
摘要：We consider an alternative implementation of the interior point methods. In the popular implementations, a variant of sparse Cholesky factorization is integrated with a conjugate gradient type iterative method. In contrast, we set up the problem as an infinitely summable series of vectors. This series is then, iteratively, summed. At each iteration, a procedure based on ''least squares'' is used to obtain an estimate of the ''tail'' of the series. In addition, using Chebychev approximations, w...
