joint work with Fengmin Xu, Yu-Hong Dai
In this talk, we consider a large scale portfolio selection problem with and without a sparsity constraint. Neutral constraints on industries are included as well as investment styles. To develop fast algorithms for the use in the real financial market, we shall expose the special structure of the problem, whose Hessian is the summation of a diagonal matrix and a low rank modification. Complexity of the algorithms are analyzed. Extensive numerical experiments are conducted, which demonstrate the efficiency of the proposed algorithms compared with some state-of-the-art solvers.
joint work with Ting Kei Pong, Hao Sun, Henry Wolkowicz
The minimum cut problem, MC, consists in partitioning the set of nodes of a graph G into k subsets of given sizes in order to minimize the number of edges cut after removing the k-th set. Previous work on this topic uses eigenvalue, semidefinite programming, SDP, and doubly non-negative bounds, DNN, with the latter giving very good, but expensive, bounds. We propose a method based on the strictly contractive Peaceman-Rachford splitting method, which can obtain the DNN bound efficiently when used in combination with regularization from facial reduction, FR. The FR allows for a natural splitting of variables in order to apply inexpensive constraints and include redundant constraints. Numerical results on random data sets and vertex separator problems show efficiency and robustness of the proposed method.
The training of generative adversarial networks suffers from cyclic behaviours. In this paper, from the simple intuition that the direction of ventripetal acceletation of an object moving in uniform circular motion is toward the center of the circle, we present simultaneous and alternating centripetal acceleration methods to alleviate the cyclic behaviours. We conduct nymerical simulations to test the effectivenes and efficiency compared with several other methods.