4. Algorithms for Convex Optimization

By Masaaki Nagahara, The University of Kitakyushu, Japan, nagahara@kitakyu-u.ac.jp

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Published: 24 Sep 2020

© 2020 Masaaki Nagahara

Abstract

In the previous chapter, we have seen that convex optimization such as ℓ1 optimization is efficiently solved by using CVX on MATLAB. Such a tool is actually very useful for small or middle scale problems. However, if you treat a very large-scale problem like image processing, CVX might be insufficient. Moreover, if you want to apply the sparsity method to control systems, you should compute sparse optimization in real time (e.g. in a few msec) with a cheap device on which MATLAB cannot be installed. In such cases, you should instead write an efficient algorithm by yourself for your specific problem. This means that you should look into the black box of the toolbox.