Roger C. E. Tan

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More than a decade ago, Bramble, Pasciak and Xu developed a framework in analyzing the multigrid methods with nonnested spaces or non-inherited quadratic forms. It was subsequently known as the BPX multigrid framework, which was widely used in the analysis of multigrid and domain decomposition methods. However, the framework has an apparent limit in the(More)
Received (received date) Revised (revised date) This paper presents an algorithm for solving a class of large scale nonlinear programming problem which is originally derived from the multi-stage stochastic convex nonlinear programming. Using the Lagrangian-dual method and the Moreau-Yosida regularization, the primal problem is neatly transformed into a(More)
In this paper a nearest doubly stochastic matrix problem is studied. This problem is to find the closest doubly stochastic matrix with the prescribed (1, 1) entry to a given matrix. According to the well-established dual theory in optimization, the dual of the underlying problem is an unconstrained differentiable but not twice differentiable convex(More)