The REPOP toolbox: tackling polynomial optimization using relative entropy relaxations
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Date
2017-07
Publication Type
Conference Paper
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yes
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Abstract
Polynomial optimization is an active field of research which can be used in a broad range of applications including the synthesis of control policies for non-linear systems, and solution methods such as approximate dynamic programming. Finding the optimal solution of a generic polynomial optimization problem remains a computationally intractable problem. Several studies in the literature resort to hierarchical schemes that converge to the optimal solution, by employing appropriate convex relaxations of the original problem. In this direction, sum of squares methods have shown to be effective in addressing problems of low degree and dimension, with numerous MATLAB toolboxes allowing for efficient implementation. An alternative solution method is to cast the problem as a signomial optimization and solve it using a hierarchy of relative entropy relaxations. In contrast to sum of squares, this method can tackle problems involving high degree and dimension polynomials. In this paper, we develop the publicly available REPOP toolbox to address polynomial optimization problems using relative entropy relaxations. The toolbox is equipped with appropriate pre-processing routines that considerably reduce the size of the resulting optimization problem. In addition, we propose a convergent hierarchy which combines aspects from sum of squares and relative entropy relaxations. The proposed method offers computational advantages over both methods.
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Publication status
published
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Book title
20th IFAC World Congress. Proceedings
Journal / series
Volume
50 (1)
Pages / Article No.
11652 - 11657
Publisher
Elsevier
Event
20th IFAC World Congress (IFAC 2017)
Edition / version
Methods
Software
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Date created
Subject
relaxations; sum-of-squares; polynomial methods; convex optimization; signomial optimization; relative entropy relaxations; matlab toolbox
Organisational unit
03751 - Lygeros, John / Lygeros, John