An Efficient Algorithm for Linear Semi-Infinite Programming over Positive Polynomials
An Efficient Algorithm for Linear Semi-Infinite Programming over Positive Polynomials
- Author(s): Meiling Xu and Zongwei Luo
- DOI: 10.1049/cp.2015.0602
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- Author(s): Meiling Xu and Zongwei Luo Source: 12th International Symposium on Operations Research and its Applications in Engineering, Technology and Management (ISORA 2015), 2015 page ()
- Conference: 12th International Symposium on Operations Research and its Applications in Engineering, Technology and Management (ISORA 2015)
- DOI: 10.1049/cp.2015.0602
- ISBN: 978-1-78561-085-1
- Location: Luoyang, China
- Conference date: 21-24 Aug. 2015
- Format: PDF
This paper describes an efficient implementation of a form of linear semi-infinite programming (LSIP). We look at maximizing (minimizing) a linear function over a set of constraints formed by positive trigonometric polynomials. Previous studies about LSIP are formulated using semi-definite programming (SDP), this is typically done by using the Kalman Yakubovich Popov (KYP) lemma or using a trace operation involving a Grammian matrix, which can be computationally expensive. The proposed algorithm is based on simplex method that directly solves the LSIP without any parameterization. Numerical results show that the proposed LISP algorithm is significantly more efficient than existing SDP solvers using KYP lemma and Grammian matrix, in both execution time and memory.
Inspec keywords: linear programming; polynomials; matrix algebra
Subjects: Algebra; Algebra; Algebra; Optimisation techniques; Optimisation techniques; Optimisation
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