Projects per year
Abstract
The overall topic of this thesis is convex conic optimization, a subfield of mathematical optimization that attacks optimization problem with a certain geometric structure. These problems allow for modelling of an extremely wide range of realworld problems, but the availability of solution algorithms for these problems is still limited.
The goal of this thesis is to investigate and shed light on two computational aspects of homogeneous interiorpoint algorithms for convex conic optimization:
The first part studies the possibility of devising a homogeneous interiorpoint method aimed at solving problems involving constraints that require nonsymmetric cones in their formulation. The second part studies the possibility of warmstarting the homogeneous interiorpoint algorithm for conic problems. The main outcome of the first part is the introduction of a completely new homogeneous interiorpoint algorithm designed to solve nonsymmetric convex conic optimization problems. The algorithm is presented in detail and then analyzed. We prove its convergence and complexity. From a theoretical viewpoint, it is fully competitive with other algorithms and from a practical viewpoint, we show that it holds lots of potential, in several cases being superior to other solution methods.
The main outcome of the second part of the thesis is two new warmstarting schemes for the homogeneous interiorpoint algorithm for conic problems. Again, we first motivate and present the schemes and then analyze them. It is proved that they, under certain circumstances, result in an improved worstcase complexity as compared to a normal coldstart. We then move on to present an extensive series of computational results substantiating the practical usefulness of these warmstarting schemes. These experiments include standard benchmarking problem test sets as well as an application from smart energy systems.
The goal of this thesis is to investigate and shed light on two computational aspects of homogeneous interiorpoint algorithms for convex conic optimization:
The first part studies the possibility of devising a homogeneous interiorpoint method aimed at solving problems involving constraints that require nonsymmetric cones in their formulation. The second part studies the possibility of warmstarting the homogeneous interiorpoint algorithm for conic problems. The main outcome of the first part is the introduction of a completely new homogeneous interiorpoint algorithm designed to solve nonsymmetric convex conic optimization problems. The algorithm is presented in detail and then analyzed. We prove its convergence and complexity. From a theoretical viewpoint, it is fully competitive with other algorithms and from a practical viewpoint, we show that it holds lots of potential, in several cases being superior to other solution methods.
The main outcome of the second part of the thesis is two new warmstarting schemes for the homogeneous interiorpoint algorithm for conic problems. Again, we first motivate and present the schemes and then analyze them. It is proved that they, under certain circumstances, result in an improved worstcase complexity as compared to a normal coldstart. We then move on to present an extensive series of computational results substantiating the practical usefulness of these warmstarting schemes. These experiments include standard benchmarking problem test sets as well as an application from smart energy systems.
Original language  English 

Place of Publication  Kgs. Lyngby 

Publisher  Technical University of Denmark 
Number of pages  149 
Publication status  Published  2013 
Series  IMMPHD2013 

Number  311 
ISSN  09093192 
Fingerprint
Dive into the research topics of 'The Homogeneous InteriorPoint Algorithm: Nonsymmetric Cones, Warmstarting, and Applications'. Together they form a unique fingerprint.Projects
 1 Finished

LargeScale Algorithms for NonSmooth Convexs Optimization
Skajaa, A., Hansen, P. C., Jørgensen, J. B., Evgrafov, A., Gondzio, J. & Vandenberghe, L.
Technical University of Denmark
01/02/2010 → 22/11/2013
Project: PhD