An entropy regularization technique for minimizing a sum of Tchebycheff norms (Q969313)

This paper studies the minimization of a sum of Tchebycheff norms. Since the original formulation of the problem yields a non-smooth objective, the authors propose a smooth approximation based on an entropy function with a smoothing parameter \(\tau\). Subsequently, the resulting smooth minimization problems are solved by a damped Newton method. Driving the smoothing parameter to zero generates a trajectory of optimal solutions that tends to the primal-dual solution set of the original minimization problem. Numerical results for several test problems are shown. Here, the algorithm proposed by the authors is compared with a primal-dual path-following interior point method proposed by \textit{Y. Zhang} [J. Optimization Theory Appl. 77, No. 2, 323--341 (1993; Zbl 0796.49029)].