Tools and Methods for Large-scale Convex Optimization

Download or read book Tools and Methods for Large-scale Convex Optimization written by Eric Chu and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex optimization is widely used in many areas of engineering science such as control theory, statistics and machine learning, and image and signal processing. There are, however, several barriers to the use of convex optimization in everyday engineering: solvers for convex optimization in general require specialized knowledge to code, and in order to solve problems, users must typically perform tedious manual transformations before calling a solver. This problem is exacerbated when problem sizes become extremely large. In this thesis, we investigate tools and methods to address these two issues in the context of large-scale convex optimization. In particular, we develop technology to handle very large problems, including a large-scale solver and a tool to model potentially large optimization problems. This tool allows users to describe their problems with an intuitive model that is automatically transformed into a form handled by the large-scale solver, liberating users from performing tedious manual transformations. For the large-scale solver, we use the alternating direction method of multipliers (ADMM) and express conic optimization problems in consensus form, splitting the linear algebra from the generalized conic inequalities. For modeling optimization problems, we present the quadratic cone modeling language (QCML), which like CVX is a tool that automatically converts convex optimization problems into conic form and solves them with a standard cone solver. Unlike CVX, QCML can be used to analyze and generate code for entire problem families without requiring another analysis or generation phase when problem (instance) data or dimensions change.