Introducing a MATLAB Toolbox for F-Lipschitz Optimization

Abstract

The theory of mathematical optimization is useful within a wide range of disciplines such as science, engineering, economics and industry. Application areas have been growing steadily, driving forward the development of new effective methods. Inspired by the need for fast computational schemes in wireless sensor networks, a new optimization theory, called Fast Lipschitz, has emerged to provide effective algorithms both for distributed and centralized computations. An important property of these algorithms is that a globally optimal solution is always guranteed. In this master thesis project, a new MATLAB toolbox is developed to check wether an optimization problem is F-Lipschitz and to solve it efficiently. The difficulty is posed in verifying that a given problem is in fact F-Lipschitz. However, it is shown that under certain circumstances, this operation has a computational complexity of O(n^2) for a problem with n decision variables. The toolbox provides both a graphical interface as well as inline functions. A user guide is presented, explaining the functionalities by discussions and illustrations of example problems. Among others, a convex optimization problem of distributed detection is considered, as well as a non-convex radio power allocation problem. The novel toolbox presented in this thesis may be of considerable utility in solving optimization problems and studying their characteristics.