An Algebraic-Based Primal–Dual Interior-Point Algorithm for Rotated Quadratic Cone Optimization

In rotated quadratic cone programming problems, we minimize a linear objective function over the intersection of an affine linear manifold with the Cartesian product of rotated quadratic cones. In this paper, we introduce the rotated quadratic cone programming problems as a “self-made” class of opti...

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Bibliographic Details
Published in:Computation 2023-03, Vol.11 (3), p.50
Main Authors: Tamsaouete, Karima, Alzalg, Baha
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Artificial intelligence
Cartesian coordinates
convex programming
interior-point methods
Jordan algebras
Linear programming
Manifolds (Mathematics)
Mathematical optimization
Mathematical programming
Optimization
Quadratic programming
rotated quadratic cone
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Summary:In rotated quadratic cone programming problems, we minimize a linear objective function over the intersection of an affine linear manifold with the Cartesian product of rotated quadratic cones. In this paper, we introduce the rotated quadratic cone programming problems as a “self-made” class of optimization problems. Based on our own Euclidean Jordan algebra, we present a glimpse of the duality theory associated with these problems and develop a special-purpose primal–dual interior-point algorithm for solving them. The efficiency of the proposed algorithm is shown by providing some numerical examples.
ISSN:2079-3197
2079-3197
DOI:10.3390/computation11030050