Multivariate spectral gradient method is proposed for solving unconstrained optimization problems. Combined with some quasi-Newton property multivariate spectral gradient method allows an individual adaptive stepsize along each coordinate direction, which guarantees that the method is finitely convergent for positive definite quadratics. Especially, it converges no more than two steps for posit...

The shrinkage method of Ledoit and Wolf (2003; 2004a; 2004b) has shown certain success in estimating a well-conditioned covariance matrix for high dimensional portfolios. This paper generalizes the shrinkage method of Ledoit and Wolf to a multivariate shrinkage setting, by which the well-conditioned covariance matrix is estimated using the weighted averaging of multiple priors, instead of singl...

The proposed “Tracking Resource Allocation Cognitive Strategies” tool (TRACS) allows for post-hoc visualization of the cognitive steps exhibited by a human operator while interacting with a multivariate resource allocation decision-support interface. This tool was applied to both mission planning for multi-criteria resource allocation for military strikes, and also multi-variable geospatial pat...

Recent years have seen many algorithmic advances in the area of submodular optimization: (SO) min /max f(S) : S ∈ F , where F is a given family of feasible sets over a ground set V and f : 2 → R is submodular. This progress has been coupled with a wealth of new applications for these models. Our focus is on a more general class of multi-agent submodular optimization (MASO) which was introduced ...