In this paper, we first propose a portfolio management model where the objective is to balance equity and liability. The asset price dynamics includes both permanent and temporary price impact, where the permanent impact is a linear function of the cumulative trading amount and the temporary...

Quadratic assignment problems (QAPs) are known to be among the most challenging discrete optimization problems. Recently, a new class of semi-definite relaxation models for QAPs based on matrix splitting has been proposed (Mittelmann and Peng, SIAM J Optim 20:3408–3426, <CitationRef CitationID="CR25">2010</CitationRef>; Peng et...</citationref>

Recently, using the framework of self-regularity, Salahi in his Ph.D. thesis proposed an adaptive single step algorithm which takes advantage of the current iterate information to find an appropriate barrier parameter rather than using a fixed fraction of the current duality gap. However, his...

This short discussion paper comments on Francisco Santos’ excellent review paper Recent Progress on the Combinatorial Diameter of Polytopes and Simplicial Complexes. We provide some notes on a few closely related topics that were not covered in the survey paper, such as: some relaxed version...