MINIMIZING A WEIGHTED BARRIER FUNCTION SUBJECT TO SECOND-ORDER CONE AND LINEAR EQUALITY CONSTRAINTS

This work concerns minimizing a weighted barrier function subject to a system of second-order cone constraints and linear equality constraints. For a given weight vector, the related barrier function is minimized using Newton’s method. We apply both quadratic interpolation and backtracking line searches. A starting point for the process is not required. A starting point is found initially as a solution to the linear system. Then, the Dmax constraint consensus method is applied to find an interior feasible point from the initial starting point. We use numerical experiments on randomly generated problems to investigate the method’s effectiveness in minimizing the weighted barrier function.