We present a new strategy for choosing primal and dual steplengths in a primal-dual interior-point algorithm for convex quadratic programming. Current implementations often scale steps equally to avoid increases in dual infeasibility between iterations. We propose that this method can be too conservative, while safeguarding an unequally-scaled steplength approach will often require fewer steps ...

This paper proposed a hybrid PSO algorithm that combines the Primal-Dual method with APSO algorithm to address the problem of swarm robotics flocking motion. This algorithm combines the explorative ability of APSO with the exploitative capacity of the Primal Dual Interior Point Method. We hypothesize that the fusion of the two algorithms (APSO and Primal Dual) offers a robust prospect of preven...

We present a new method which solves a double-barelled LASSO in a convex least squares approach. In the presented method we focus on the scenario where one is interested in (or limited to) a primal (feature) representation for the first view while having a dual (kernel) representation for the second view. DB-LASSO minimises the number of features used in both the primal and dual projections whi...

We show existence and uniqueness of a solution for the non-local vector-valued Allen-Cahn variational inequality in a formulation involving Lagrange multipliers for local and non-local constraints. Furthermore, we propose and analyze a primal-dual active set method for local and non-local vector-valued Allen-Cahn variational inequalities. Convergence of the primal-dual active set algorithm is s...